title: Central America

text: In the Pre-Columbian era, the northern areas of Central America were inhabited by the indigenous peoples of Mesoamerica. Most notable among these were the Mayans, who had built numerous cities throughout the region, and the Aztecs, who had created a vast empire. The pre-Columbian cultures of eastern El Salvador, eastern Honduras, Caribbean Nicaragua, most of Costa Rica and Panama were predominantly speakers of the Chibchan languages at the time of European contact and are considered by some culturally different and grouped in the Isthmo-Colombian Area.


title: Central America

text: Following the Spanish expedition of Christopher Columbus's voyages to the Americas, the Spanish sent many expeditions to the region, and they began their conquest of Maya territory in 1523. Soon after the conquest of the Aztec Empire, Spanish conquistador Pedro de Alvarado commenced the conquest of northern Central America for the Spanish Empire. Beginning with his arrival in Soconusco in 1523, Alvarado's forces systematically conquered and subjugated most of the major Maya kingdoms, including the K'iche', Tz'utujil, Pipil, and the Kaqchikel. By 1528, the conquest of Guatemala was nearly complete, with only the Petén Basin remaining outside the Spanish sphere of influence. The last independent Maya kingdoms – the Kowoj and the Itza people – were finally defeated in 1697, as part of the Spanish conquest of Petén.


title: Central America

text: In 1538, Spain established the Real Audiencia of Panama, which had jurisdiction over all land from the Strait of Magellan to the Gulf of Fonseca. This entity was dissolved in 1543, and most of the territory within Central America then fell under the jurisdiction of the "Audiencia Real de Guatemala". This area included the current territories of Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Mexican state of Chiapas, but excluded the lands that would become Belize and Panama. The president of the Audiencia, which had its seat in Antigua Guatemala, was the governor of the entire area. In 1609 the area became a captaincy general and the governor was also granted the title of captain general. The Captaincy General of Guatemala encompassed most of Central America, with the exception of present-day Belize and Panama.


title: Central America

text: The Captaincy General of Guatemala lasted for more than two centuries, but began to fray after a rebellion in 1811 which began in the Intendancy of San Salvador. The Captaincy General formally ended on 15 September 1821, with the signing of the Act of Independence of Central America. Mexican independence was achieved at virtually the same time with the signing of the Treaty of Córdoba and the Declaration of Independence of the Mexican Empire, and the entire region was finally independent from Spanish authority by 28 September 1821.


title: Central America

text: From its independence from Spain in 1821 until 1823, the former Captaincy General remained intact as part of the short-lived First Mexican Empire. When the Emperor of Mexico abdicated on 19 March 1823, Central America again became independent. On 1 July 1823, the Congress of Central America peacefully seceded from Mexico and declared absolute independence from all foreign nations, and the region formed the Federal Republic of Central America.


title: Central America

text: The Federal Republic of Central America was a representative democracy with its capital at Guatemala City. This union consisted of the provinces of Costa Rica, El Salvador, Guatemala, Honduras, Los Altos, Mosquito Coast, and Nicaragua. The lowlands of southwest Chiapas, including Soconusco, initially belonged to the Republic until 1824, when Mexico annexed most of Chiapas and began its claims to Soconusco. The Republic lasted from 1823 to 1838, when it disintegrated as a result of civil wars.


title: Central America

text: The territory that now makes up Belize was heavily contested in a dispute that continued for decades after Guatemala achieved independence (see History of Belize (1506–1862). Spain, and later Guatemala, considered this land a Guatemalan department. In 1862, Britain formally declared it a British colony and named it British Honduras. It became independent as Belize in 1981.


title: Central America

text: Panama, situated in the southernmost part of Central America on the Isthmus of Panama, has for most of its history been culturally and politically linked to South America. Panama was part of the Province of Tierra Firme from 1510 until 1538 when it came under the jurisdiction of the newly formed "Audiencia Real de Panama". Beginning in 1543, Panama was administered as part of the Viceroyalty of Peru, along with all other Spanish possessions in South America. Panama remained as part of the Viceroyalty of Peru until 1739, when it was transferred to the Viceroyalty of New Granada, the capital of which was located at Santa Fé de Bogotá. Panama remained as part of the Viceroyalty of New Granada until the disestablishment of that viceroyalty in 1819. A series of military and political struggles took place from that time until 1822, the result of which produced the republic of Gran Colombia. After the dissolution of Gran Colombia in 1830, Panama became part of a successor state, the Republic of New Granada. From 1855 until 1886, Panama existed as Panama State, first within the Republic of New Granada, then within the Granadine Confederation, and finally within the United States of Colombia. The United States of Colombia was replaced by the Republic of Colombia in 1886. As part of the Republic of Colombia, Panama State was abolished and it became the Isthmus Department. Despite the many political reorganizations, Colombia was still deeply plagued by conflict, which eventually led to the secession of Panama on 3 November 1903. Only after that time did some begin to regard Panama as a North or Central American entity.


title: Central America

text: By the 1930s the United Fruit Company owned of land in Central America and the Caribbean and was the single largest land owner in Guatemala. Such holdings gave it great power over the governments of small countries. That was one of the factors that led to the coining of the phrase banana republic.


title: Central America

text: After more than two hundred years of social unrest, violent conflict, and revolution, Central America today remains in a period of political transformation. Poverty, social injustice, and violence are still widespread. Nicaragua is the second poorest country in the western hemisphere (only Haiti is poorer).


title: Central America

text: Central America is a part of North America consisting of a tapering isthmus running from the southern extent of Mexico to the northwestern portion of South America. Central America has the Gulf of Mexico, a body of water within the Atlantic Ocean, to the north; the Caribbean Sea, also part of the Atlantic Ocean, to the northeast; and the Pacific Ocean to the southwest. Some physiographists define the Isthmus of Tehuantepec as the northern geographic border of Central America, while others use the northwestern borders of Belize and Guatemala. From there, the Central American land mass extends southeastward to the Atrato River, where it connects to the Pacific Lowlands in northwestern South America.


title: Central America

text: Of the many mountain ranges within Central America, the longest are the Sierra Madre de Chiapas, the Cordillera Isabelia and the Cordillera de Talamanca. At , Volcán Tajumulco is the highest peak in Central America. Other high points of Central America are as listed in the table below:


title: Central America

text: Between the mountain ranges lie fertile valleys that are suitable for the raising of livestock and for the production of coffee, tobacco, beans and other crops. Most of the population of Honduras, Costa Rica and Guatemala lives in valleys.


title: Central America

text: Trade winds have a significant effect upon the climate of Central America. Temperatures in Central America are highest just prior to the summer wet season, and are lowest during the winter dry season, when trade winds contribute to a cooler climate. The highest temperatures occur in April, due to higher levels of sunlight, lower cloud cover and a decrease in trade winds.


title: Central America

text: Central America is part of the Mesoamerican biodiversity hotspot, boasting 7% of the world's biodiversity. The Pacific Flyway is a major north–south flyway for migratory birds in the Americas, extending from Alaska to Tierra del Fuego. Due to the funnel-like shape of its land mass, migratory birds can be seen in very high concentrations in Central America, especially in the spring and autumn. As a bridge between North America and South America, Central America has many species from the Nearctic and the Neotropical realms. However the southern countries (Costa Rica and Panama) of the region have more biodiversity than the northern countries (Guatemala and Belize), meanwhile the central countries (Honduras, Nicaragua and El Salvador) have the least biodiversity. The table below shows recent statistics:


title: Central America

text: Over 300 species of the region's flora and fauna are threatened, 107 of which are classified as critically endangered. The underlying problems are deforestation, which is estimated by FAO at 1.2% per year in Central America and Mexico combined, fragmentation of rainforests and the fact that 80% of the vegetation in Central America has already been converted to agriculture.


title: Central America

text: Efforts to protect fauna and flora in the region are made by creating ecoregions and nature reserves. 36% of Belize's land territory falls under some form of official protected status, giving Belize one of the most extensive systems of terrestrial protected areas in the Americas. In addition, 13% of Belize's marine territory are also protected. A large coral reef extends from Mexico to Honduras: the Mesoamerican Barrier Reef System. The Belize Barrier Reef is part of this. The Belize Barrier Reef is home to a large diversity of plants and animals, and is one of the most diverse ecosystems of the world. It is home to 70 hard coral species, 36 soft coral species, 500 species of fish and hundreds of invertebrate species.


title: Central America

text: From 2001 to 2010, of forest were lost in the region. In 2010 Belize had 63% of remaining forest cover, Costa Rica 46%, Panama 45%, Honduras 41%, Guatemala 37%, Nicaragua 29%, and El Salvador 21%. Most of the loss occurred in the moist forest biome, with . Woody vegetation loss was partially set off by a gain in the coniferous forest biome with , and a gain in the dry forest biome at . Mangroves and deserts contributed only 1% to the loss in forest vegetation. The bulk of the deforestation was located at the Caribbean slopes of Nicaragua with a loss of of forest in the period from 2001 to 2010. The most significant regrowth of of forest was seen in the coniferous woody vegetation of Honduras.


title: Central America

text: The Central American pine-oak forests ecoregion, in the tropical and subtropical coniferous forests biome, is found in Central America and southern Mexico. The Central American pine-oak forests occupy an area of , extending along the mountainous spine of Central America, extending from the Sierra Madre de Chiapas in Mexico's Chiapas state through the highlands of Guatemala, El Salvador, and Honduras to central Nicaragua. The pine-oak forests lie between elevation, and are surrounded at lower elevations by tropical moist forests and tropical dry forests. Higher elevations above are usually covered with Central American montane forests. The Central American pine-oak forests are composed of many species characteristic of temperate North America including oak, pine, fir, and cypress.


title: Central America

text: Laurel forest is the most common type of Central American temperate evergreen cloud forest, found in almost all Central American countries, normally more than above sea level. Tree species include evergreen oaks, members of the laurel family, species of "Weinmannia" and "Magnolia", and "Drimys granadensis". The cloud forest of Sierra de las Minas, Guatemala, is the largest in Central America. In some areas of southeastern Honduras there are cloud forests, the largest located near the border with Nicaragua. In Nicaragua, cloud forests are situated near the border with Honduras, but many were cleared to grow coffee. There are still some temperate evergreen hills in the north. The only cloud forest in the Pacific coastal zone of Central America is on the Mombacho volcano in Nicaragua. In Costa Rica, there are laurel forests in the Cordillera de Tilarán and Volcán Arenal, called Monteverde, also in the Cordillera de Talamanca.


title: Central America

text: The Central American montane forests are an ecoregion of the tropical and subtropical moist broadleaf forests biome, as defined by the World Wildlife Fund. These forests are of the moist deciduous and the semi-evergreen seasonal subtype of tropical and subtropical moist broadleaf forests and receive high overall rainfall with a warm summer wet season and a cooler winter dry season. Central American montane forests consist of forest patches located at altitudes ranging from , on the summits and slopes of the highest mountains in Central America ranging from Southern Mexico, through Guatemala, El Salvador, and Honduras, to northern Nicaragua. The entire ecoregion covers an area of and has a temperate climate with relatively high precipitation levels.


title: Central America

text: Ecoregions are not only established to protect the forests themselves but also because they are habitats for an incomparably rich and often endemic fauna. Almost half of the bird population of the Talamancan montane forests in Costa Rica and Panama are endemic to this region. Several birds are listed as threatened, most notably the resplendent quetzal (Pharomacrus mocinno), three-wattled bellbird (Procnias tricarunculata), bare-necked umbrellabird (Cephalopterus glabricollis), and black guan (Chamaepetes unicolor). Many of the amphibians are endemic and depend on the existence of forest. The golden toad that once inhabited a small region in the Monteverde Reserve, which is part of the Talamancan montane forests, has not been seen alive since 1989 and is listed as extinct by IUCN. The exact causes for its extinction are unknown. Global warming may have played a role, because the development of that frog is typical for this area may have been compromised. Seven small mammals are endemic to the Costa Rica-Chiriqui highlands within the Talamancan montane forest region. Jaguars, cougars, spider monkeys, as well as tapirs, and anteaters live in the woods of Central America. The Central American red brocket is a brocket deer found in Central America's tropical forest.


title: Central America

text: Central America is geologically very active, with volcanic eruptions and earthquakes occurring frequently, and tsunamis occurring occasionally. Many thousands of people have died as a result of these natural disasters.


title: Central America

text: Most of Central America rests atop the Caribbean Plate. This tectonic plate converges with the Cocos, Nazca, and North American plates to form the Middle America Trench, a major subduction zone. The Middle America Trench is situated some off the Pacific coast of Central America and runs roughly parallel to it. Many large earthquakes have occurred as a result of seismic activity at the Middle America Trench. For example, subduction of the Cocos Plate beneath the North American Plate at the Middle America Trench is believed to have caused the 1985 Mexico City earthquake that killed as many as 40,000 people. Seismic activity at the Middle America Trench is also responsible for earthquakes in 1902, 1942, 1956, 1982, 1992, January 2001, February 2001, 2007, 2012, 2014, and many other earthquakes throughout Central America.


title: Central America

text: The Middle America Trench is not the only source of seismic activity in Central America. The Motagua Fault is an onshore continuation of the Cayman Trough which forms part of the tectonic boundary between the North American Plate and the Caribbean Plate. This transform fault cuts right across Guatemala and then continues offshore until it merges with the Middle America Trench along the Pacific coast of Mexico, near Acapulco. Seismic activity at the Motagua Fault has been responsible for earthquakes in 1717, 1773, 1902, 1976, 1980, and 2009.


title: Central America

text: Another onshore continuation of the Cayman Trough is the Chixoy-Polochic Fault, which runs parallel to, and roughly to the north, of the Motagua Fault. Though less active than the Motagua Fault, seismic activity at the Chixoy-Polochic Fault is still thought to be capable of producing very large earthquakes, such as the 1816 earthquake of Guatemala.


title: Central America

text: Volcanic eruptions are also common in Central America. In 1968 the Arenal Volcano, in Costa Rica, erupted killing 87 people as the 3 villages of Tabacon, Pueblo Nuevo and San Luis were buried under pyroclastic flows and debris. Fertile soils from weathered volcanic lava have made it possible to sustain dense populations in the agriculturally productive highland areas.


title: Central America

text: The population of Central America is estimated at as of . With an area of , it has a population density of . Human Development Index values are from the estimates for 2017.


title: Central America

text: The official language majority in all Central American countries is Spanish, except in Belize, where the official language is English. Mayan languages constitute a language family consisting of about 26 related languages. Guatemala formally recognized 21 of these in 1996. Xinca, Miskito, and Garifuna are also present in Central America.


title: Central America

text: This region of the continent is very rich in terms of ethnic groups. The majority of the population is mestizo, with sizable Mayan and African descendent populations present, including Xinca and Garifuna minorities. The immigration of Arabs, Jews, Chinese, Europeans and others brought additional groups to the area.


title: Central America

text: The predominant religion in Central America is Christianity (95.6%). Beginning with the Spanish colonization of Central America in the 16th century, Roman Catholicism became the most popular religion in the region until the first half of the 20th century. Since the 1960s, there has been an increase in other Christian groups, particularly Protestantism, as well as other religious organizations, and individuals identifying themselves as having no religion.


title: Central America

text: Central America is currently undergoing a process of political, economic and cultural transformation that started in 1907 with the creation of the Central American Court of Justice.


title: Central America

text: In 1951 the integration process continued with the signature of the San Salvador Treaty, which created the ODECA, the Organization of Central American States. However, the unity of the ODECA was limited by conflicts between several member states.


title: Central America

text: In 1991, the integration agenda was further advanced by the creation of the Central American Integration System ("Sistema para la Integración Centroamericana", or SICA). SICA provides a clear legal basis to avoid disputes between the member states. SICA membership includes the 7 nations of Central America plus the Dominican Republic, a state that is traditionally considered part of the Caribbean.


title: Central America

text: On 6 December 2008, SICA announced an agreement to pursue a common currency and common passport for the member nations. No timeline for implementation was discussed.


title: Central America

text: Central America already has several supranational institutions such as the Central American Parliament, the Central American Bank for Economic Integration and the Central American Common Market.


title: Central America

text: On 22 July 2011, President Mauricio Funes of El Salvador became the first president "pro tempore" to SICA. El Salvador also became the headquarters of SICA with the inauguration of a new building.


title: Central America

text: Until recently, all Central American countries maintained diplomatic relations with Taiwan instead of China. President Óscar Arias of Costa Rica, however, established diplomatic relations with China in 2007, severing formal diplomatic ties with Taiwan. After breaking off relations with the Republic of China in 2017, Panama established diplomatic relations with the People's Republic of China. In August 2018, El Salvador also severed ties with Taiwan to formally start recognizing the People's Republic of China as sole China, a move many considered lacked transparency due to its abruptness and reports of the Chinese government's desires to invest in the department of La Union while also promising to fund the ruling party's reelection campaign. The President of El Salvador, Nayib Bukele, broke diplomatic relations with Taiwan and established ties with China. On 9 December 2021, Nicaragua resumed relations with the PRC.


title: Central America

text: The Central American Parliament (aka PARLACEN) is a political and parliamentary body of SICA. The parliament started around 1980, and its primary goal was to resolve conflicts in Nicaragua, Guatemala, and El Salvador. Although the group was disbanded in 1986, ideas of unity of Central Americans still remained, so a treaty was signed in 1987 to create the Central American Parliament and other political bodies. Its original members were Guatemala, El Salvador, Nicaragua and Honduras. The parliament is the political organ of Central America, and is part of SICA. New members have since then joined including Panama and the Dominican Republic.


title: Central America

text: Costa Rica is not a member State of the Central American Parliament and its adhesion remains as a very unpopular topic at all levels of the Costa Rican society due to existing strong political criticism towards the regional parliament, since it is regarded by Costa Ricans as a menace to democratic accountability and effectiveness of integration efforts. Excessively high salaries for its members, legal immunity of jurisdiction from any member State, corruption, lack of a binding nature and effectiveness of the regional parliament's decisions, high operative costs and immediate membership of Central American Presidents once they leave their office and presidential terms, are the most common reasons invoked by Costa Ricans against the Central American Parliament.


title: Central America

text: Signed in 2004, the Central American Free Trade Agreement (CAFTA) is an agreement between the United States, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Dominican Republic. The treaty is aimed at promoting free trade among its members.


title: Central America

text: Guatemala has the largest economy in the region. Its main exports are coffee, sugar, bananas, petroleum, clothing, and cardamom. Of its 10.29 billion dollar annual exports, 40.2% go to the United States, 11.1% to neighboring El Salvador, 8% to Honduras, 5.5% to Mexico, 4.7% to Nicaragua, and 4.3% to Costa Rica.


title: Central America

text: The region is particularly attractive for companies (especially clothing companies) because of its geographical proximity to the United States, very low wages and considerable tax advantages. In addition, the decline in the prices of coffee and other export products and the structural adjustment measures promoted by the international financial institutions have partly ruined agriculture, favouring the emergence of maquiladoras. This sector accounts for 42 per cent of total exports from El Salvador, 55 per cent from Guatemala, and 65 per cent from Honduras. However, its contribution to the economies of these countries is disputed; raw materials are imported, jobs are precarious and low-paid, and tax exemptions weaken public finances.


title: Central America

text: They are also criticised for the working conditions of employees: insults and physical violence, abusive dismissals (especially of pregnant workers), working hours, non-payment of overtime. According to Lucrecia Bautista, coordinator of the "maquilas" sector of the audit firm Coverco, "labour law regulations are regularly violated in maquilas and there is no political will to enforce their application. In the case of infringements, the labour inspectorate shows remarkable leniency. It is a question of not discouraging investors". Trade unionists are subject to pressure, and sometimes to kidnapping or murder. In some cases, business leaders have used the services of the maras. Finally, black lists containing the names of trade unionists or political activists are circulating in employers' circles.


title: Central America

text: Economic growth in Central America is projected to slow slightly in 2014–15, as country-specific domestic factors offset the positive effects from stronger economic activity in the United States.


title: Central America

text: Tourism in Belize has grown considerably in more recent times, and it is now the second largest industry in the nation. Belizean Prime Minister Dean Barrow has stated his intention to use tourism to combat poverty throughout the country. The growth in tourism has positively affected the agricultural, commercial, and finance industries, as well as the construction industry. The results for Belize's tourism-driven economy have been significant, with the nation welcoming almost one million tourists in a calendar year for the first time in its history in 2012. Belize is also the only country in Central America with English as its official language, making this country a comfortable destination for English-speaking tourists.


title: Central America

text: Costa Rica is the most visited nation in Central America. Tourism in Costa Rica is one of the fastest growing economic sectors of the country, having become the largest source of foreign revenue by 1995. Since 1999, tourism has earned more foreign exchange than bananas, pineapples and coffee exports combined. The tourism boom began in 1987, with the number of visitors up from 329,000 in 1988, through 1.03 million in 1999, to a historical record of 2.43 million foreign visitors and $1.92-billion in revenue in 2013. In 2012 tourism contributed with 12.5% of the country's GDP and it was responsible for 11.7% of direct and indirect employment.


title: Central America

text: Tourism in Nicaragua has grown considerably recently, and it is now the second largest industry in the nation. Nicaraguan President Daniel Ortega has stated his intention to use tourism to combat poverty throughout the country. The growth in tourism has positively affected the agricultural, commercial, and finance industries, as well as the construction industry. The results for Nicaragua's tourism-driven economy have been significant, with the nation welcoming one million tourists in a calendar year for the first time in its history in 2010.


title: Central America

text: The Inter-American Highway is the Central American section of the Pan-American Highway, and spans between Nuevo Laredo, Mexico, and Panama City, Panama. Because of the break in the highway known as the Darién Gap, it is not possible to cross between Central America and South America in an automobile.


title: Google Photos

text: Google Photos is a photo sharing and storage service developed by Google. It was announced in May 2015 and spun off from Google+, the company's former social network.


title: Google Photos

text: As of June 1, 2021, in its free tier, any newly uploaded photo and video counts towards the 15 GB free storage quota shared across the user's Google services, with the exception of current Pixel phones. The previous free tier, unlimited photos and videos up to 16 megapixels and 1080p resolution respectively (anything larger gets down-scaled to these sizes), ended on the same day.


title: Google Photos

text: The service automatically analyzes photos, identifying various visual features and subjects. Users can search for anything in photos, with the service returning results from three major categories: People, Places, and Things. The computer vision of Google Photos recognizes faces (not only those of humans, but pets as well), grouping similar ones together (this feature is only available in certain countries due to privacy laws); geographic landmarks (such as the Eiffel Tower); and subject matter, including birthdays, buildings, animals, food, and more.


title: Google Photos

text: Different forms of machine learning in the Photos service allow recognition of photo contents, automatically generate albums, animate similar photos into quick videos, surface past memories at significant times, and improve the quality of photos and videos. In May 2017, Google announced several updates to Google Photos, including reminders for and suggested sharing of photos, shared photo libraries between two users, and physical albums. Photos automatically suggested collections based on face, location, trip, or other distinction.


title: Google Photos

text: Google Photos received critical acclaim after its decoupling from Google+ in 2015. Reviewers praised the updated Photos service for its recognition technology, search, apps, and loading times. Nevertheless, privacy concerns were raised, including Google's motivation for building the service, as well as its relationship to governments and possible laws requiring Google to hand over a user's entire photo history. Google Photos has seen strong user adoption. It reached 100 million users after five months, 200 million after one year, 500 million after two years, and passed the 1 billion user mark in 2019, four years after its initial launch. Google reports as of 2020, approximately 28 billion photos and videos are uploaded to the service every week, and more than 4 trillion photos are stored in the service total.


title: Google Photos

text: Google Photos is the standalone successor to the photo features previously embedded in Google+, the company's social network. Google launched the social network to compete with Facebook, but the service never became as popular as Facebook for social networking and photo sharing. Google+ offered photo storage and organizational tools that surpassed Facebook's in power, though Google+ lacked the user base to use it. By leaving the social network affiliation, the Photos service changed its association from a sharing platform to a private library platform.


title: Google Photos

text: In December 2015, Google added shared albums to Google Photos. Users pool photos and videos into an album, and then share the album with other Google Photos users. The recipient "can join to add their own photos and videos, and also get notifications when new pics are added". Users can also save photos and videos from shared albums to add them to their own, private collection. Unlike the native Photos service within iOS, Google Photos permits full resolution sharing across Android and iOS platforms and between the two.


title: Google Photos

text: On February 12, 2016, Google announced that the Picasa desktop application would be discontinued on March 15, 2016, followed by the closure of the Picasa Web Albums service on May 1, 2016. Google stated that the primary reason for retiring Picasa was that it wanted to focus its efforts "entirely on a single photo service"; the cross-platform, web-based Google Photos.


title: Google Photos

text: In June 2016, Google updated Photos to include automatically generated albums. After an event or trip, Photos will group some of the photos together and suggest creating an album with them, alongside maps to show geographic travel and location pins for exact places. Users can also add text captions to describe photos. In October, Google announced multiple significant updates; Google Photos now surfaces old memories with people identified in users' recent photos; it occasionally highlights a subset of photos when a user has recently taken a lot of images of a specific subject; it now makes animations from videos as well as photos (photo animations have been present since the start), displaying specific photos intermixed with short excerpts from longer videos in videos; and it now attempts to detect sideways and upside down photos and prompts the user to accept or reject a different orientation. For all of these features, Google touts machine learning does the work, with no user interaction required.


title: Google Photos

text: In November, Google released a separate app - PhotoScan - for users to scan printed photos into the service. The app, released for iOS and Android, uses a scanning process in which users must center their camera over four dots that overlay the printed image, so that the software can combine the photographs for a high-resolution digital image with the fewest possible defects. Later that month, Google added a "Deep blue" slider feature that lets users change the color and saturation of skies, without degrading image quality or inadvertently changing colors of other objects or elements in photos.


title: Google Photos

text: In February 2017, Google updated the "Albums" tab on the Android app to include three separate sections; one for the phone's camera roll, with different views for sorting options (such as people or location); another for photos taken inside other apps; and a third for the actual photo albums. In March, Google added an automatic white balance feature to the service. The Android app and website were the first to receive the feature, with a later rollout to the iOS app. Later in March, updates to the service enabled uploading of photos in a "lightweight preview" quality for immediate viewing on slow cellular networks before a higher-quality upload later while on faster Wi-Fi. The feature also extends to sharing photos, in which a low-resolution image will be sent before being updated with a higher-quality version. In April, Google added video stabilization. The feature creates a duplicate video to avoid overwriting the original clip.


title: Google Photos

text: In May 2017, Google announced several updates to Google Photos. "Suggested Sharing" reminds users to share captured photos after the fact, and also groups photos based on faces and suggests recipients based on facial recognition. "Shared Libraries" lets two users share a central repository for all photos or specific categories of images. "Photo Books" are physical collections of photos, offered either as softcover or hardcover albums, with Photos automatically suggesting collections based on face, location, trip, or other distinction. Towards the end of the month, Google introduced an "Archive" feature that lets users hide photos from the main timeline view without deleting them. Archived content still appears in relevant albums and in search. In June, the new sharing features announced in May began rolling out to users.


title: Google Photos

text: In December 2018, Google doubled the number of photos and videos users can store in a private Google Photos Live Album. The number increased from 10,000 to 20,000 photos, which is equivalent to the capacity for shared albums.


title: Google Photos

text: In September 2019, Google Photos introduced a new social media-like feature called "Memories" similar to the Stories feature in Instagram and Facebook which highlights past photos to give their users a nostalgic feeling.


title: Google Photos

text: On June 25, 2020, Google Photos introduced a major redesign to the mobile and web apps, accompanied by a new, simplified logo.


title: Google Photos

text: The service has apps for the Android and iOS operating systems, and a website. Users back up their photos to the cloud service, which becomes accessible for all of their devices.


title: Google Photos

text: The Photos service analyzes and organizes images into groups and can identify features such as beaches, skylines, or "snowstorm in Toronto." From the application's search window, users are shown potential searches for groups of photos in three major categories: People, Places, and Things. The service analyzes photos for similar faces and groups them together in the People category. It can also track faces as they age. The Places category uses geotagging data but can also determine locations in older pictures by analyzing for major landmarks (e.g., photos containing the Eiffel Tower). The Things category processes photos for their subject matter: birthdays, buildings, cats, concerts, food, graduations, posters, screenshots, etc. Users can manually remove categorization errors. Google Lens is also integrated into the service.


title: Google Photos

text: Recipients of shared images can view web galleries without needing to download the app. Users can swipe their fingers across the screen to adjust the service's photo editing settings, as opposed to using sliders. Images can be easily shared with social networks (Google+, Facebook, Twitter) and other services. The application generates web links that both Google Photos users and non-users can access.


title: Google Photos

text: There are issues about data sharing and exporting, such as not being able to download pictures and videos in their original quality or with all the original data, notably GPS location info. Even downloading via the Google Takeout feature results in some of the original information missing. This could potentially lead to vendor lock in if the user wants to keep using features requiring those missing pieces of data.


title: Google Photos

text: Google Photos has three storage settings: "High quality" (now Storage Saver), "Original quality" and "Express quality" (unavailable in certain locations). High quality includes photo and video storage for photos up to 16 megapixels and videos up to 1080p resolution (the maximum resolutions for average smartphone users in 2015). Original quality preserves the original resolution and quality of the photos and videos. Express quality includes photo and video storage for photos up to 3 megapixels and videos up to 480p resolution.


title: Google Photos

text: For the first three generations of the Google Pixel phones, Google Photos offers unlimited storage at "Original quality" for free. The original Pixel had no limits to this offer, while the Pixel 2 and 3 only offered unlimited storage at "Original quality" for photos and videos taken before January 16, 2021 and January 31, 2022 respectively, with all photos and videos taken after those dates being uploaded at "High quality" instead. The Pixel 3a and onwards do not offer unlimited storage at "Original quality", with the Pixel 4, Pixel 4a, Pixel 4a (5G), and Pixel 5 offering a 3-month trial for the 100 GB Google One plan to new members instead.


title: Google Photos

text: In November 2020, Google Photos announced that it would be ending its offering of free unlimited storage for photos uploaded in "high quality" or "express quality" starting on June 1, 2021, due to rising demand for storage. On June 1, 2021, Google Photos changed the name of "high quality" to "storage saver". The move was part of an effort to reduce Google's reliance on ad-based revenue and increase subscriptions. Existing photos will remain unaffected, and new photos will count towards the user's storage quota shared across Google Drive, Gmail, and Google Photos. Owners of the first five generations of Google Pixel smartphones will remain exempt from this change.


title: Google Photos

text: In October 2015, five months after the launch of the service, Google announced that Google Photos had 100 million users, who had uploaded 3.72 petabytes of photos and videos.


title: Google Photos

text: In May 2016, one year after the release of Google Photos, Google announced the service had over 200 million monthly active users. Other statistics it revealed was at least 13.7 petabytes of photos/videos had been uploaded, 2 trillion labels had been applied (24 billion of those being selfies), and 1.6 billion animations, collages and effects had been created based on user content.


title: Google Photos

text: In May 2017, Google announced that Google Photos has over 500 million users, who upload over 1.2 billion photos every day.


title: Google Photos

text: In November 2020, Google announced that more than 4 trillion photos are stored in Google Photos, and every week 28 billion new photos and videos are uploaded.


title: Google Photos

text: At the May 2015 release of Google Photos, reviewers wrote that the service was among the best of its kind. Walt Mossberg of "Recode" declared the service the best in cloud photo storage, against its competition from Amazon (Amazon Drive), Apple (iCloud), Dropbox, and Microsoft (OneDrive). Jacob Kastrenakes of "The Verge" wrote that the release made Google a major competitor in the photo storage market, and that its pricing structure obsoleted the idea of paying for photo storage. Sarah Mitroff and Lynn La of "CNET" wrote that the service's phone and tablet apps were particularly good, and that Google Photos had a more streamlined design than Yahoo's Flickr and more organizing features than Apple's iCloud photo service.


title: Google Photos

text: Kastrenakes described the service's May 2015 release as evidence that Google was spinning out the "best features" of its Google+ social network. He stated that the Photos service was "always excellent", and liked that users would be able to use the service "without signing up for a new social network". Mossberg described the release as "liberation day" for the photos features that were "effectively hidden" in the "widely ignored social network". The service's strategy, as described by Josh Lowensohn of "The Verge", was to put all data on Google's servers so that it can be accessed universally.


title: Google Photos

text: Mossberg liked the service's search function, writing that a search for "Massachusetts" "instantly brought up loads of photos of subjects". Lowensohn noted the service's speed and intelligence, especially in its ability to sort unorganized photos, as well as its photo loading times, search speeds, and simple photo editing tools. Kastrenakes compared the service's new image analysis to technology unveiled by Flickr earlier in the same month. Mossberg thought the face grouping feature was "remarkably accurate", but was most impressed by the subject-based grouping. He was surprised that a search for "boats" found both Cape Cod fishing boats and Venetian gondolas, but also noted errors such as a professional photograph registering as a screenshot.


title: Google Photos

text: "PC Magazine" John C. Dvorak was concerned about the service's privacy. He was particularly concerned about Google's motivation for building the service, the company's relationships with existing governments, and potential laws that would require Google to provide a user's entire history of photos upon request. Dvorak compared such a scenario to inviting others to "scrounge through your underwear drawer". He criticized the service's sync functions, and preferred folders of images over an unsorted "flat database". Dvorak also highlighted the service's poor choice of photos to animate and lack of longevity guarantees, considering the company's abrupt cancellation of Google Reader. He ultimately suggested that users instead use a portable hard drive, which he considered safer and cheap.


title: Ukrainian Ground Forces

text: The Ukrainian Ground Forces (), also known as the Ukrainian Army, are the land forces of Ukraine and one of the five branches of the Armed Forces of Ukraine. They were formed from Soviet Ground Forces formations, units, and establishments, including three military districts (the Kyiv, Carpathian, and Odesa Military Districts), that were on Ukrainian soil when the Soviet Union collapsed.


title: Ukrainian Ground Forces

text: After Ukraine's independence from the Soviet Union in 1991, Ukraine retained its Soviet-era army equipment. The Armed Forces were systematically downsized after 1991 and as a result, it was largely dilapidated by July 2014. Since the start of the war in Donbas in April 2014 in eastern Ukraine, Ukraine embarked on a program to enlarge and modernize its Armed Forces. Its size of 129,950 in March 2014 had grown to 204,000 active personnel in May 2015, with the Ground Forces branch having 169,000 soldiers as of 2016. In 2016, 75% of the army consisted of contract servicemen. Ukraine's ground forces have also received more modern tanks, APCs, and many other types of combat equipment.


title: Ukrainian Ground Forces

text: Prior to the October Revolution of 1917, three separate self-governing Ukrainian states existed on what is Ukraine today. Each of these states possessed armed forces. The largest of these, the Ukrainian People's Republic, itself comprised three separate regimes. The Ukrainian People's Army is an example of one of the early national armed forces. Other armed independence movements existed in the wake of both the First World War and the Second World War, and these armies each had distinct organisation and uniforms. These armed forces, and the independent Ukrainian homeland for which they fought, were eventually incorporated into the neighboring states of Poland, Soviet Union, Hungary, Romania and Czechoslovakia.


title: Ukrainian Ground Forces

text: Upon their establishment in 1991, the Armed Forces of Ukraine included approximately 780,000 personnel, 7,000 armored vehicles, 6,500 tanks, and 2,500 tactical nuclear missiles. A problem that Ukraine faced was that while it had vast armed forces, it lacked a proper command structure. On 24 August 1991, the Verkhovna Rada of Ukraine ratified a resolution taking control of all military units of the former Soviet Armed Forces situated on the territory of Ukraine. This established the Ministry of Defence of Ukraine.


title: Ukrainian Ground Forces

text: Following the declaration of Ukrainian independence in 1991, Ukraine inherited the 1st Guards Army, 13th Army, 38th Army, two tank armies (the 6th Guards Tank Army and the 8th Tank Army), and the 32nd Army Corps at Simferopol. The 28th Guards Motor Rifle Division and the 180th Rifle Division were left in Ukraine, having been previously under the 14th Guards Army headquartered at Tiraspol in the Moldovan SSR. The post of commander of ground troops was designated in early 1992. By the end of 1992, the Kyiv Military District disbanded, and Ukraine used its structures as the basis for the Ministry of Defence and the General Staff.


title: Ukrainian Ground Forces

text: Between June and August 1993, the first redesignation of armies to army corps appears to have taken place. While the chief of ground forces post had been created in early 1992, it was over two years before the first holder, Colonel General Vasily Sobkov, was appointed on 7 April 1994. The legal framework for the Ground Forces was defined in Article 4 of the law 'On the Armed Forces of Ukraine.' At that time, the Ground Forces had no separate command body, and were directly subordinate to the Ukrainian General Staff.


title: Ukrainian Ground Forces

text: The creation of the Ground Forces as a separate armed service was enacted by Presidential Decree 368/96 of 23 May 1996, 'On the Ground Forces of Ukraine.' That year both the Ground Forces Command was formed and the 1st Army Corps was reorganised as the Northern Territorial Operational Command (which became the Northern Operational Command in 1998). In 1997 the Carpathian Military District was reorganised as the Western Operational Command.From 1992 to 1997, the forces of the Kyiv MD were transferred to the Odessa MD, and the Odessa MD's headquarters moved to Donetsk. A new 2nd Army Corps was formed in the Odessa MD. Armies were converted to army corps, and motor rifle divisions converted into mechanised divisions or brigades. Pairs of attack helicopter regiments were combined to form army aviation brigades.


title: Ukrainian Ground Forces

text: President Leonid Kuchma revealed in a December 1996 speech that as many as 191 mechanised infantry and tank battalions were rated not ready, adding,"This is especially dangerous in the forward-based units securing the nation's borders."


title: Ukrainian Ground Forces

text: Under a plan promulgated in 2000 the Ground Forces were to reduce the number of troops from the then 300,000 to 240,000 by 2015, and an ultimate change from a partial conscript-based force to a fully professional military. The Armed Forces received little more than half of the Hr 68 million it was promised for reform in 2001, but managed to disband nine regiments and close 21 local military bases.


title: Ukrainian Ground Forces

text: In 2005–06, the Northern Operational Command was reorganised as Territorial Directorate "North". It was tasked with territorial defence, mobilisation training, and preparation of reserves.


title: Ukrainian Ground Forces

text: From 1991 the Ukrainian Ground Forces bought its military equipment only from Russia and other CIS states, as well as locally producing some of their own equipment. Until 2014 and the start of the war in Donbas, the defence industry in Ukraine produced equipment mostly for export.


title: Ukrainian Ground Forces

text: In the aftermath of the 2014 Ukrainian Revolution, Russian special forces in unmarked uniforms began surrounding Ukrainian military bases on the Crimean peninsula before capturing them individually using a mixture of attrition and threats. Over the following weeks the Russian Armed Forces consolidated control of the peninsula and established road blocks to cut off the possibility of Ukraine sending reinforcements from the mainland. The takeover of Crimea was largely bloodless, as the Ukrainian soldiers didn't retaliate. By the end of March, all remaining Ukrainian troops were ordered to pull out of Crimea.


title: Ukrainian Ground Forces

text: The Ukrainian Army was considered to be in a poor state during and after the annexation, with only 6,000 of its troops ready for combat and many of its vehicles lacking batteries. After Russia's annexation only 6,000 of the 20,300 Ukrainian soldiers stationed in Crimea before the annexation left the peninsula. The rest stayed in Crimea and defected to Russia.


title: Ukrainian Ground Forces

text: In the early months of the war in Donbas that erupted in 2014 the Armed Forces were widely criticised for their poor equipment and inept leadership, forcing Internal Affairs Ministry forces like the National Guard and the territorial defence battalions to take on the brunt of the fighting in the first months of the war.


title: Ukrainian Ground Forces

text: By February 2018 the Ukrainian armed forces were larger and better equipped, numbering 200,000 active-service military personnel. Most of the volunteer soldiers of the territorial defence battalions were integrated into the official Ukrainian army.


title: Ukrainian Ground Forces

text: Within the reporting period of 16 November 2017 to 15 February 2018 a United Nations OHCHR monitoring mission documented 115 cases of credible allegations of human rights abuses committed on both sides of the contact line. The nature of the crimes ranges from enforced disappearances, looting of civilian property, torture, rape and sexual violence up to political repression and extrajudicial killings.


title: Ukrainian Ground Forces

text: On 24 February 2022, Russia began a full-scale invasion of Ukraine. The Ground Forces have been participants of most of the land combat actions of the current war. The influx of Western materiel and supplies to the branch before and during the conflict as well as mobilization efforts have resulted in a massive expansion of the force, in addition to ongoing force modernization.


title: Ukrainian Ground Forces

text: Training in 2006 was aimed at developing mobility and combat readiness of the forces. The Ukrainian armed forces took advantage of the opportunities provided by UN exercises and exercises where Ukraine and NATO nations and other partners participated.


title: Ukrainian Ground Forces

text: Training resulted in 6,000 combat-ready troops in the spring of 2014 of Ukraine's (then) 129,950 active military personnel. In 2016 the Ukrainian army had more than 200,000 combat-ready soldiers of its 260,000 active personnel.


title: Ukrainian Ground Forces

text: In 2015 Ukraine, the United States, the United Kingdom and Canada established the Joint Multinational Training Group – Ukraine (JMTG-U) and they set up three new training sites, in Khmelnytskyi, Kamianets-Podilskyi, and Yavoriv. The latter, known as the International Center for Peacekeeping and Security or the Yavoriv Combat Training Center, was hit by eight Russian missiles in March 2022.


title: Ukrainian Ground Forces

text: It appears that the SAS has left behind forces to train Ukrainian soldiers. At least two of the officers from the SAS were confirmed as having been in Ukraine. Each posted with a different battalion near Kyiv. There emphasis has been training Ukrainian soldiers how to use the Anglo-Swedish NLAW. Other soldiers have actually been trained in the UK, according to the article. It would appear that the training course is approximately two weeks long for each participant.


title: Ukrainian Ground Forces

text: This follows an earlier report of UK special forces being left behind in Ukraine. This includes the SAS, Special Boat Service and Special Reconnaissance Regiment. The other contributors appear to be unnamed special forces from Eastern European countries. These forces are training the Ukrainian military in sabotage, counter-insurgency and sniping.


title: Ukrainian Ground Forces

text: In 2007 the system of exercise/training ranges was optimized, decreasing their number and providing a specialized role.


title: Ukrainian Ground Forces

text: Mechanised Infantry and armoured forces are the primary components of the Ukrainian Ground Forces. Their primary objectives in case of war are capturing and holding targets, maintaining positions, defending against attack, penetrating enemy lines and defeating enemy forces.


title: Ukrainian Ground Forces

text: The mechanised and armoured forces are equipped with a combination of Soviet-made (part of them modernized) and modern Ukrainian armored vehicles which includes T-80, T-64, (T-64BV Model 2017, T-64BV), T-64BM "Bulat" and T-72UA1 main battle tanks, BTR-4, BTR-60, BTR-70 and BTR-80 wheeled armored personnel carriers and BMP-1, BMP-2 and BMD-2 infantry combat vehicles.


title: Ukrainian Ground Forces

text: Since the fall of the Soviet Union, a large number of the previous Soviet mechanised formations on Ukrainian soil have been disbanded – the IISS says totals have dropped from 14 divisions, in 1992, to two divisions, six brigades, and one independent regiment in 2008. Today, all mechanised and armoured formations are called brigades.


title: Ukrainian Ground Forces

text: The Ukrainian Ground Forces also include two mountain infantry brigades and the newly formed 61st Jager brigade, reformed from the 61st Motorized Infantry in 2019.


title: Ukrainian Ground Forces

text: Army Aviation provides reconnaissance, tactical fire support and air transport for the Ukrainian Ground Forces. As of 2017 Ukraine's army fields four Army Aviation brigades in an Army Aviation Command directly subordinated to the Ground Forces HQ:


title: Ukrainian Ground Forces

text: The Army Aviation's maintenance facility is the 57th Aviation Base in Brody. The service's equipment includes: Mi-2, Mi-8, Mi-9, Mi-24 and Mi-26 helicopters.


title: Ukrainian Ground Forces

text: The Army Air Defence units are responsible for protecting troops against enemy air attacks anywhere on the battlefield, and while in combat. The Ukrainian Ground Forces army air defence branch is equipped with a variety of effective surface-to-air missile systems of division level and anti-aircraft missile and artillery complexes of regiment level. Regiment level units are characterized by their high rate of fire, vitality, maneuverability, and capability of action under all conditions of modern combat arms operations. Surface-to-air missile systems and complexes of division level are characterized by their long range and firepower and are equipped with surface-to-air missile complexes; S-300V, Osa, Buk, Buk-M1 and Tor. While anti-aircraft missile and artillery complexes that are of regiment level are equipped with the Tunguska-M1, Igla MANPADS system, Strela, and Shilka anti-aircraft missile systems.The army's only separate radar system, meaning it isn't a part of any anti-aircraft system, is the Ukrainian Kolchuga-M. It was designed sometime between the years 1993–1997, the system is said to be one of the most advanced passive sensors in the world, as it is claimed to be able to detect stealth aircraft.


title: Ukrainian Ground Forces

text: The Donbas war caused a radical reform of the Ukrainian Armed Forces in the general and the Ukrainian Ground Forces in particular. It built and expanded on the 2011 structure. As of 2022 the structure is the following:


title: Ukrainian Ground Forces

text: The Operational Command West (MU А0796) is headquartered in Rivne and has an area of responsibility covering the Volyn, Zakarpattia, Ivano-Frankivsk, Lviv, Rivne, Ternopil, Khmelnytskyi and Chernivtsi Oblasts.


title: Ukrainian Ground Forces

text: The Operational Command North (MU 4583) is headquartered in Chernihiv and has an area of responsibility covering the Zhytomyr, Kyiv, Poltava, Sumy, Cherkasy and Chernihiv Oblasts and the capital city of Kyiv.


title: Ukrainian Ground Forces

text: The Operational Command South (MU 2393) is headquartered in Odesa and has an area of responsibility covering the Vinnytsia, Kirovohrad, Mykolaiv, Odesa and Kherson Oblasts.


title: Ukrainian Ground Forces

text: The Operational Command East (MU 1314) is headquartered in Dnipro and has an area of responsibility covering Dnipropetrovsk, Donetsk, Zaporizhzhia, Luhansk, and Kharkiv Oblasts with the Russian-occupied territory of the Crimea nominally attached to it as the Separate Ground Forces Area ("Окремий військово-сухопутний район"). OC East is the general command responsible for frontline regular UGF formations fighting in the War in Donbas and the current Russian invasion.


title: Ukrainian Ground Forces

text: The army's Reserve Corps (Ukrainian: "Корпус резерву") is a new formation, directly subordinated to the General Staff. It is also called the Army Strategic Reserve Corps. Its main function is to prepare and administer the reservists of the ground forces. According to plans it should be fully operational by 2020 with reserve servicemen in three separate categories:


title: Ukrainian Ground Forces

text: In that organization the Reserve Corps is currently (2022) engaged in the ongoing Russian invasion of Ukraine, and its reservists have fought in every ground operation of the conflict.


title: Ukrainian Ground Forces

text: In the new uniforms the Ukrainian Ground Forces unveiled in August 2016 the stars that traditionally adorn shoulder straps have been replaced by diamonds. A new set of insignia are being adopted.


title: Ukrainian Ground Forces

text: The Ukrainian Army unveiled its new uniforms on 24 August 2016 (Independence Day of Ukraine). The new uniforms are modeled on British military styles, having a modern pixelated digital camouflage pattern. They also incorporate details from the uniforms worn by the Ukrainian People's Army. The new cap includes an insignia of a Ukrainian Cossack grasping a cross.


title: Ukrainian Ground Forces

text: Ukraine deployed a sizable contingent of troops to the Iraq War, these were stationed near Kut. Ukraine's troop deployment was the second largest of all former Soviet states besides Georgia and they deployed more soldiers to the nation then many members of NATO such as Estonia, Latvia, and Lithuania. Ukraine also suffered the fifth highest casualty toll during the war, with only Polish, Italian, UK, and US forces suffering heavier losses.


title: Ukrainian Ground Forces

text: From 2003 to 2005 over 1,700 Ukrainian soldiers were deployed to Iraq, the third-largest contingent at the time, they were designated to the 5th Mechanized Brigade, as in Ukraine's mission to Kosovo the troops deployed were contract soldiers and not conscripts. Ukraine began to severely draw down its troop levels in Iraq in 2005 due to mounting casualties and the political toxicity of the conflict. By 2005 only 876 soldiers, roughly half of the original contingent were deployed, by years end troop levels dropped to below 100. In 2008, one year before the official end of the US military mission, President Viktor Yushchenko ordered all remaining troops deployed to Iraq to be returned home and Ukraine's mission to the nation officially over.


title: Ukrainian Ground Forces

text: Between 2001 and 2021, Ukraine allowed United States military cargo planes to fly over and refuel on Ukrainian soil on their way to Afghanistan. In 2007 Ukraine deployed a detachment of the 143rd De-mining Center of the Armed Forces of Ukraine to Afghanistan. Ukraine has kept a team of soldiers deployed to Afghanistan as part of ISAF since 2007, these mostly consisted of pilots, medical officers, and bomb disposal experts.


title: Ukrainian Ground Forces

text: Ukrainian pilots were responsible for training the pilots of the Afghan Air Force on the operation of several air craft as Afghanistan's forces consisted of many Soviet designed aircraft such as the Mi-17, which Ukrainian troops were very familiar with. In 2013, the contingent of troops in Afghanistan totaled 26 troops. As of 2014 the Ukrainian contingent was further drawn down and the team included 8 bomb disposal experts and several medical officers.


title: Ukrainian Ground Forces

text: Ukrainian forces have also been deployed to Kosovo since 2000 as part of the 600 man Polish–Ukrainian Peace Force Battalion. In August 2014, Ukraine ended its mission to Kosovo due to the 2014 Russian invasion of Ukraine.


title: Ukrainian Ground Forces

text: Ukrainian peacekeeping forces have been deployed to the Democratic Republic of Congo, Liberia, Sudan and South Sudan and Cote d'Ivoire. Ukrainian forces have also been requested to take a more active role in the Northern Mali Conflict of 2012 in battling Islamic forces. One of the largest deployments is the 18th Separate Helicopter Unit of the Armed Forces of Ukraine which consisted of 160 servicemen and four Mi-24P helicopters and was deployed to the Democratic Republic of Congo in 2011.


title: Ukrainian Ground Forces

text: Ukraine provides combat veterans with various benefits. Ukrainians who have served in World War II, the Soviet–Afghan War, or as liquidators at the Chernobyl disaster are eligible for benefits such as a monthly allowance, a discount on medical and pharmacy services, free use of public transportation, additional vacation days from work, having priority for retention in case of work layoffs, easier loan access and approval process, preference when applying for security related positions, priority when applying to vocation school or trade school, and electricity, gas, and housing subsidies. Veterans are also eligible to stay at military sanatoriums, provided there is available space.


title: Ukrainian Ground Forces

text: Since gaining independence, Ukraine has deployed troops to Kosovo, Iraq, and Afghanistan, gaining a new generation of veterans separate from those who served in the Soviet forces. Most recently the government passed a law extending veteran benefits to Ukrainian troops participating in the war in Donbas. Veterans from other nations who move to or reside in Ukraine may be eligible for some of the listed benefits. This provision was likely made to ensure that World War II, Chernobyl, and Afghanistan veterans from other Soviet states who moved to Ukraine received similar benefits. As Ukraine has participated in numerous NATO led conflicts since its independence it is unclear if NATO veterans would be extended these benefits.


title: Ukrainian Ground Forces

text: Veteran groups are not as developed as in the United States which has numerous well known national organizations such as the Veterans of Foreign Wars. World War II veterans, and even persons who have lived through the war are generally treated with the highest respect. Other veterans are not as well known. Ukrainian veterans from the Soviet War of Afghanistan are strikingly similar to the Vietnam veterans of the United States, although the Soviet Union generally kept the public in the dark through the war, unlike in Vietnam, where coverage was very high. Afghanistan is often labeled as a mistake by the Soviet Union and its successor states, but the lack of media coverage, and the censorship through the war have ensured that many still remain unaware of their nation's involvement in the conflict. Despite Ukraine having the 3rd largest contingent of troops in Iraq in 2004, few also realize that their nation has many veterans of the Iraq war.


title: Emile Hirsch

text: Emile Davenport Hirsch (born March 13, 1985) is an American actor. He played Chris McCandless in "Into the Wild" (2007). Other notable film roles include "The Girl Next Door" (2004), "Lords of Dogtown" (2005), "Alpha Dog" (2006), "Speed Racer" (2008), "Milk" (2008), "Lone Survivor" (2013), "An Evening with Beverly Luff Linn" (2018), and "Once Upon a Time in Hollywood" (2019).


title: Emile Hirsch

text: Hirsch is of German, English, and Scots-Irish ancestry; he was born in the Palms section of Los Angeles. His mother, Margaret Esther (née Davenport), is a visual artist, teacher, and pop-up book designer, and his father, David Milton Hirsch, is an entrepreneur, manager, and producer. He has an older sister, Jennifer, and was raised in Los Angeles and Santa Fe, New Mexico, where he lived with his mother for several years. Hirsch attended at Alexander Hamilton High School where he studied in the Music program.


title: Emile Hirsch

text: Hirsch began acting on television roles in the late 1990s. He starred in the Showtime original film "Wild Iris" (2001), with Laura Linney and Gena Rowlands. He made his film debut for "The Dangerous Lives of Altar Boys" (2002) and next acted with Kevin Kline in "The Emperor's Club" (2002).


title: Emile Hirsch

text: In 2004, Hirsch starred in "The Girl Next Door". He starred with Jeff Daniels and Sigourney Weaver in the limited release "Imaginary Heroes" (2004). In 2005, Hirsch starred in Catherine Hardwicke's film "Lords of Dogtown" (2005) about a group of skaters in the 1970s and their role in the birth of skateboard culture. Hirsch played Jay Adams. He played a character based on a real-life drug dealer, Jesse James Hollywood, in "Alpha Dog" (2006).


title: Emile Hirsch

text: Hirsch played Christopher McCandless in "Into the Wild" (2007). He lost 40 pounds for the role, which earned him a Screen Actors Guild nomination for best actor. "Esquire" said, "[Hirsch] creates a vivid, unforgettable character you at once admire and pity."


title: Emile Hirsch

text: Hirsch had the title role in the Wachowskis' "Speed Racer", which was released on May 9, 2008 and was a box office bomb. Hirsch played gay-rights activist Cleve Jones in Gus Van Sant's biopic "Milk" (2008). He also appeared in Ang Lee's "Taking Woodstock" (2009), based on a screenplay of the Elliot Tiber memoir "Taking Woodstock". He then starred in the William Friedkin's 2011 southern gothic thriller "Killer Joe".


title: Emile Hirsch

text: In 2012, Hirsch starred with Penélope Cruz in "Venuto al Mondo", a film by Italian director Sergio Castellitto. In 2013, he was in "Prince Avalanche", co-starring Paul Rudd.


title: Emile Hirsch

text: Hirsch starred in "The Motel Life", co-starring Dakota Fanning and Stephen Dorff, directed by the Polsky brothers. In 2013, he starred with Holliday Grainger, Holly Hunter, and William Hurt in the miniseries "Bonnie & Clyde". Hirsch co-starred in the film "Lone Survivor", based on the memoir of Navy SEAL Marcus Luttrell.


title: Emile Hirsch

text: In February 2017, it was announced that Hirsch would star with Aubrey Plaza in the comedy "An Evening with Beverly Luff Linn".


title: Emile Hirsch

text: In May 2018, Hirsch became the new voice for character James Lake Jr. in the Netflix original DreamWorks show "" from Guillermo del Toro, replacing Anton Yelchin in its third season following his death in 2016. Hirsch continues to reprise the role of Jim in "3 Below", "" and "".


title: Emile Hirsch

text: In 2019, Hirsch portrayed Hollywood hairdresser and Manson family victim Jay Sebring in the film "Once Upon a Time in Hollywood".


title: Emile Hirsch

text: On October 25, 2019, Hirsch released his first album under Hirsch called Mnemonic. Two of its songs, Tooth Fairy and Angels Will, were selected to be on the New Alt playlist on Spotify. KROQ DJ Megan Holiday also picked Mnemonic as one of her favorite albums of the year. After Mnemonic's release, Hirsch released the single "American Dreamin'", and on 2/14 released his new single "Casual Animal."


title: Emile Hirsch

text: Hirsch has recently released five singles, "Remember Days When," (which he co-wrote with Foster The People's Mark Foster) and "Hard Hearts" (both on 03/13/20). He released Prisoners on 03/27/20 & "The Same Different" on 04/03/20, and then "Favors" on 05/08/20. Both "Prisoners" and "Favors" were both put on Spotify's New Noise Playlist. "Favors" was also put on multiple playlists on Deezer, including #3 placement on "Seleccíon Editorial Mexico y Central America," one of Deezer's biggest playlists worldwide, with 6.7 million followers.


title: Emile Hirsch

text: After releasing a couple of new singles over a year, Hirsch released his second album called Denihilism on March 12, 2021.


title: Emile Hirsch

text: On October 27, 2013, Hirsch's first child was born, a boy named Valor. The child's mother is a woman Hirsch dated; however, they are no longer in a relationship.


title: Emile Hirsch

text: On February 12, 2015, Hirsch was charged with aggravated assault after attacking and strangling Paramount Pictures executive Daniele Bernfeld on January 25, 2015, at Tao Nightclub in Park City, Utah. Hirsch claimed he did not remember what had happened as the event happened when he was taking stimulants while inebriated. On August 17, 2015, he pleaded guilty to misdemeanor assault and was sentenced to 15 days in jail. He was also fined $4,750, received 90 days of probation, and was ordered to undergo 50 hours of community service. Hirsch entered a rehab facility following the assault.


title: Quantum entanglement

text: Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.


title: Quantum entanglement

text: Measurements of physical properties such as position, momentum, spin, and polarization performed on entangled particles can, in some cases, be found to be perfectly correlated. For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be anticlockwise. However, this behavior gives rise to seemingly paradoxical effects: any measurement of a particle's properties results in an irreversible wave function collapse of that particle and changes the original quantum state. With entangled particles, such measurements affect the entangled system as a whole.


title: Quantum entanglement

text: Such phenomena were the subject of a 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen, and several papers by Erwin Schrödinger shortly thereafter, describing what came to be known as the EPR paradox. Einstein and others considered such behavior impossible, as it violated the local realism view of causality (Einstein referring to it as "spooky action at a distance") and argued that the accepted formulation of quantum mechanics must therefore be incomplete.


title: Quantum entanglement

text: Later, however, the counterintuitive predictions of quantum mechanics were verified in tests where polarization or spin of entangled particles was measured at separate locations, statistically violating Bell's inequality. In earlier tests, it could not be ruled out that the result at one point could have been subtly transmitted to the remote point, affecting the outcome at the second location. However, so-called "loophole-free" Bell tests have been performed where the locations were sufficiently separated that communications at the speed of light would have taken longer—in one case, 10,000 times longer—than the interval between the measurements.


title: Quantum entanglement

text: According to "some" interpretations of quantum mechanics, the effect of one measurement occurs instantly. Other interpretations which do not recognize wavefunction collapse dispute that there is any "effect" at all. However, all interpretations agree that entanglement produces correlation between the measurements and that the mutual information between the entangled particles can be exploited, but that any transmission of information at faster-than-light speeds is impossible.


title: Quantum entanglement

text: Quantum entanglement has been demonstrated experimentally with photons, neutrinos, electrons, molecules as large as buckyballs, and even small diamonds. The utilization of entanglement in communication, computation and quantum radar is a very active area of research and development.


title: Quantum entanglement

text: In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper on the counterintuitive predictions that quantum mechanics makes for pairs of objects prepared together in a particular way.


title: Quantum entanglement

text: In this study, the three formulated the Einstein–Podolsky–Rosen paradox (EPR paradox), a thought experiment that attempted to show that "the quantum-mechanical description of physical reality given by wave functions is not complete."


title: Quantum entanglement

text: However, the three scientists did not coin the word "entanglement", nor did they generalize the special properties of the quantum state they considered. Following the EPR paper, Erwin Schrödinger wrote a letter to Einstein in German in which he used the word "Verschränkung" (translated by himself as "entanglement") "to describe the correlations between two particles that interact and then separate, as in the EPR experiment."


title: Quantum entanglement

text: Schrödinger shortly thereafter published a seminal paper defining and discussing the notion of "entanglement." In the paper, he recognized the importance of the concept, and stated: "I would not call [entanglement] "one" but rather "the" characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."


title: Quantum entanglement

text: Like Einstein, Schrödinger was dissatisfied with the concept of entanglement, because it seemed to violate the speed limit on the transmission of information implicit in the theory of relativity. Einstein later famously derided entanglement as ""spukhafte Fernwirkung"" or "spooky action at a distance."


title: Quantum entanglement

text: The EPR paper generated significant interest among physicists, which inspired much discussion about the foundations of quantum mechanics (perhaps most famously Bohm's interpretation of quantum mechanics), but produced relatively little other published work. Despite the interest, the weak point in EPR's argument was not discovered until 1964, when John Stewart Bell proved that one of their key assumptions, the principle of locality, as applied to the kind of hidden variables interpretation hoped for by EPR, was mathematically inconsistent with the predictions of quantum theory.


title: Quantum entanglement

text: Specifically, Bell demonstrated an upper limit, seen in Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and showed that quantum theory predicts violations of this limit for certain entangled systems. His inequality is experimentally testable, and there have been numerous relevant experiments, starting with the pioneering work of Stuart Freedman and John Clauser in 1972 and Alain Aspect's experiments in 1982. An early experimental breakthrough was due to Carl Kocher, who already in 1967 presented an apparatus in which two photons successively emitted from a calcium atom were shown to be entangled – the first case of entangled visible light. The two photons passed diametrically positioned parallel polarizers with higher probability than classically predicted but with correlations in quantitative agreement with quantum mechanical calculations. He also showed that the correlation varied as the squared cosine of the angle between the polarizer settings and decreased exponentially with time lag between emitted photons. Kocher’s apparatus, equipped with better polarizers, was used by Freedman and Clauser who could confirm the cosine-squared dependence and use it to demonstrate a violation of Bell’s inequality for a set of fixed angles. All these experiments have shown agreement with quantum mechanics rather than the principle of local realism.


title: Quantum entanglement

text: For decades, each had left open at least one loophole by which it was possible to question the validity of the results. However, in 2015 an experiment was performed that simultaneously closed both the detection and locality loopholes, and was heralded as "loophole-free"; this experiment ruled out a large class of local realism theories with certainty. Aspect writes that "... no experiment ... can be said to be totally loophole-free," but he says the experiments "remove the last doubts that we should renounce" local hidden variables, and refers to examples of remaining loopholes as being "far fetched" and "foreign to the usual way of reasoning in physics."


title: Quantum entanglement

text: Bell's work raised the possibility of using these super-strong correlations as a resource for communication. It led to the 1984 discovery of quantum key distribution protocols, most famously BB84 by Charles H. Bennett and Gilles Brassard and E91 by Artur Ekert. Although BB84 does not use entanglement, Ekert's protocol uses the violation of a Bell's inequality as a proof of security.


title: Quantum entanglement

text: In 2022, the Nobel Prize in Physics was awarded to Aspect, Clauser, and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".


title: Quantum entanglement

text: An entangled system is defined to be one whose quantum state cannot be factored as a product of states of its local constituents; that is to say, they are not individual particles but are an inseparable whole. In entanglement, one constituent cannot be fully described without considering the other(s). The state of a composite system is always expressible as a sum, or superposition, of products of states of local constituents; it is entangled if this sum cannot be written as a single product term.


title: Quantum entanglement

text: Quantum systems can become entangled through various types of interactions. For some ways in which entanglement may be achieved for experimental purposes, see the section below on methods. Entanglement is broken when the entangled particles decohere through interaction with the environment; for example, when a measurement is made.


title: Quantum entanglement

text: As an example of entanglement: a subatomic particle decays into an entangled pair of other particles. The decay events obey the various conservation laws, and as a result, the measurement outcomes of one daughter particle must be highly correlated with the measurement outcomes of the other daughter particle (so that the total momenta, angular momenta, energy, and so forth remains roughly the same before and after this process). For instance, a spin-zero particle could decay into a pair of spin-1/2 particles. Since the total spin before and after this decay must be zero (conservation of angular momentum), whenever the first particle is measured to be spin up on some axis, the other, when measured on the same axis, is always found to be spin down. (This is called the spin anti-correlated case; and if the prior probabilities for measuring each spin are equal, the pair is said to be in the singlet state.)


title: Quantum entanglement

text: The above result may or may not be perceived as surprising. A classical system would display the same property, and a hidden variable theory would certainly be required to do so, based on conservation of angular momentum in classical and quantum mechanics alike. The difference is that a classical system has definite values for all the observables all along, while the quantum system does not. In a sense to be discussed below, the quantum system considered here seems to acquire a probability distribution for the outcome of a measurement of the spin along any axis of the other particle upon measurement of the first particle. This probability distribution is in general different from what it would be without measurement of the first particle. This may certainly be perceived as surprising in the case of spatially separated entangled particles.


title: Quantum entanglement

text: The paradox is that a measurement made on either of the particles apparently collapses the state of the entire entangled system—and does so instantaneously, before any information about the measurement result could have been communicated to the other particle (assuming that information cannot travel faster than light) and hence assured the "proper" outcome of the measurement of the other part of the entangled pair. In the Copenhagen interpretation, the result of a spin measurement on one of the particles is a collapse into a state in which each particle has a definite spin (either up or down) along the axis of measurement. The outcome is taken to be random, with each possibility having a probability of 50%. However, if both spins are measured along the same axis, they are found to be anti-correlated. This means that the random outcome of the measurement made on one particle seems to have been transmitted to the other, so that it can make the "right choice" when it too is measured.


title: Quantum entanglement

text: The distance and timing of the measurements can be chosen so as to make the interval between the two measurements spacelike, hence, any causal effect connecting the events would have to travel faster than light. According to the principles of special relativity, it is not possible for any information to travel between two such measuring events. It is not even possible to say which of the measurements came first. For two spacelike separated events and there are inertial frames in which is first and others in which is first. Therefore, the correlation between the two measurements cannot be explained as one measurement determining the other: different observers would disagree about the role of cause and effect.


title: Quantum entanglement

text: A possible resolution to the paradox is to assume that quantum theory is incomplete, and the result of measurements depends on predetermined "hidden variables". The state of the particles being measured contains some hidden variables, whose values effectively determine, right from the moment of separation, what the outcomes of the spin measurements are going to be. This would mean that each particle carries all the required information with it, and nothing needs to be transmitted from one particle to the other at the time of measurement. Einstein and others (see the previous section) originally believed this was the only way out of the paradox, and the accepted quantum mechanical description (with a random measurement outcome) must be incomplete.


title: Quantum entanglement

text: Local hidden variable theories fail, however, when measurements of the spin of entangled particles along different axes are considered. If a large number of pairs of such measurements are made (on a large number of pairs of entangled particles), then statistically, if the local realist or hidden variables view were correct, the results would always satisfy Bell's inequality. A number of experiments have shown in practice that Bell's inequality is not satisfied. However, prior to 2015, all of these had loophole problems that were considered the most important by the community of physicists. When measurements of the entangled particles are made in moving relativistic reference frames, in which each measurement (in its own relativistic time frame) occurs before the other, the measurement results remain correlated.


title: Quantum entanglement

text: The fundamental issue about measuring spin along different axes is that these measurements cannot have definite values at the same time―they are incompatible in the sense that these measurements' maximum simultaneous precision is constrained by the uncertainty principle. This is contrary to what is found in classical physics, where any number of properties can be measured simultaneously with arbitrary accuracy. It has been proven mathematically that compatible measurements cannot show Bell-inequality-violating correlations, and thus entanglement is a fundamentally non-classical phenomenon.


title: Quantum entanglement

text: The first experiment that verified Einstein's "spooky action at a distance" or entanglement was successfully corroborated in a lab by Chien-Shiung Wu and a colleague named I. Shaknov in 1949, and was published on new year's day in 1950. The result specifically proved the quantum correlations of a pair of photons. In experiments in 2012 and 2013, polarization correlation was created between photons that never coexisted in time. The authors claimed that this result was achieved by entanglement swapping between two pairs of entangled photons after measuring the polarization of one photon of the early pair, and that it proves that quantum non-locality applies not only to space but also to time.


title: Quantum entanglement

text: In three independent experiments in 2013, it was shown that classically communicated separable quantum states can be used to carry entangled states. The first loophole-free Bell test was held by Ronald Hanson of the Delft University of Technology in 2015, confirming the violation of Bell inequality.


title: Quantum entanglement

text: In August 2014, Brazilian researcher Gabriela Barreto Lemos and team were able to "take pictures" of objects using photons that had not interacted with the subjects, but were entangled with photons that did interact with such objects. Lemos, from the University of Vienna, is confident that this new quantum imaging technique could find application where low light imaging is imperative, in fields like biological or medical imaging.


title: Quantum entanglement

text: Since 2016, various companies, for example IBM and Microsoft, have successfully created quantum computers that allowed developers and tech enthusiasts to freely experiment with concepts of quantum mechanics including quantum entanglement.


title: Quantum entanglement

text: There have been suggestions to look at the concept of time as an emergent phenomenon that is a side effect of quantum entanglement.


title: Quantum entanglement

text: In other words, time is an entanglement phenomenon, which places all equal clock readings (of correctly prepared clocks, or of any objects usable as clocks) into the same history. This was first fully theorized by Don Page and William Wootters in 1983.


title: Quantum entanglement

text: The Wheeler–DeWitt equation that combines general relativity and quantum mechanics – by leaving out time altogether – was introduced in the 1960s and it was taken up again in 1983, when Page and Wootters made a solution based on quantum entanglement. Page and Wootters argued that entanglement can be used to measure time.


title: Quantum entanglement

text: Based on AdS/CFT correspondence, Mark Van Raamsdonk suggested that spacetime arises as an emergent phenomenon of the quantum degrees of freedom that are entangled and live in the boundary of the space-time. Induced gravity can emerge from the entanglement first law.


title: Quantum entanglement

text: In the media and popular science, quantum non-locality is often portrayed as being equivalent to entanglement. While this is true for pure bipartite quantum states, in general entanglement is only necessary for non-local correlations, but there exist mixed entangled states that do not produce such correlations. A well-known example is the Werner states that are entangled for certain values of formula_1, but can always be described using local hidden variables. Moreover, it was shown that, for arbitrary numbers of particles, there exist states that are genuinely entangled but admit a local model.


title: Quantum entanglement

text: The mentioned proofs about the existence of local models assume that there is only one copy of the quantum state available at a time. If the particles are allowed to perform local measurements on many copies of such states, then many apparently local states (e.g., the qubit Werner states) can no longer be described by a local model. This is, in particular, true for all distillable states. However, it remains an open question whether all entangled states become non-local given sufficiently many copies.


title: Quantum entanglement

text: In short, entanglement of a state shared by two particles is necessary but not sufficient for that state to be non-local. It is important to recognize that entanglement is more commonly viewed as an algebraic concept, noted for being a prerequisite to non-locality as well as to quantum teleportation and to superdense coding, whereas non-locality is defined according to experimental statistics and is much more involved with the foundations and interpretations of quantum mechanics.


title: Quantum entanglement

text: The following subsections are for those with a good working knowledge of the formal, mathematical description of quantum mechanics, including familiarity with the formalism and theoretical framework developed in the articles: bra–ket notation and mathematical formulation of quantum mechanics.


title: Quantum entanglement

text: Consider two arbitrary quantum systems and , with respective Hilbert spaces and . The Hilbert space of the composite system is the tensor product


title: Quantum entanglement

text: If the first system is in state formula_3 and the second in state formula_4, the state of the composite system is


title: Quantum entanglement

text: States of the composite system that can be represented in this form are called separable states, or product states.


title: Quantum entanglement

text: Not all states are separable states (and thus product states). Fix a basis formula_6 for and a basis formula_7 for . The most general state in is of the form


title: Quantum entanglement

text: This state is separable if there exist vectors formula_9 so that formula_10 yielding formula_11 and formula_12 It is inseparable if for any vectors formula_13 at least for one pair of coordinates formula_14 we have formula_15 If a state is inseparable, it is called an 'entangled state'.


title: Quantum entanglement

text: For example, given two basis vectors formula_16 of and two basis vectors formula_17 of , the following is an entangled state:


title: Quantum entanglement

text: If the composite system is in this state, it is impossible to attribute to either system or system a definite pure state. Another way to say this is that while the von Neumann entropy of the whole state is zero (as it is for any pure state), the entropy of the subsystems is greater than zero. In this sense, the systems are "entangled". This has specific empirical ramifications for interferometry. The above example is one of four Bell states, which are (maximally) entangled pure states (pure states of the space, but which cannot be separated into pure states of each and ).


title: Quantum entanglement

text: Now suppose Alice is an observer for system , and Bob is an observer for system . If in the entangled state given above Alice makes a measurement in the formula_19 eigenbasis of , there are two possible outcomes, occurring with equal probability:


title: Quantum entanglement

text: If the former occurs, then any subsequent measurement performed by Bob, in the same basis, will always return 1. If the latter occurs, (Alice measures 1) then Bob's measurement will return 0 with certainty. Thus, system has been altered by Alice performing a local measurement on system . This remains true even if the systems and are spatially separated. This is the foundation of the EPR paradox.


title: Quantum entanglement

text: The outcome of Alice's measurement is random. Alice cannot decide which state to collapse the composite system into, and therefore cannot transmit information to Bob by acting on her system. Causality is thus preserved, in this particular scheme. For the general argument, see no-communication theorem.


title: Quantum entanglement

text: As mentioned above, a state of a quantum system is given by a unit vector in a Hilbert space. More generally, if one has less information about the system, then one calls it an 'ensemble' and describes it by a density matrix, which is a positive-semidefinite matrix, or a trace class when the state space is infinite-dimensional, and has trace 1. Again, by the spectral theorem, such a matrix takes the general form:


title: Quantum entanglement

text: where the "w" are positive-valued probabilities (they sum up to 1), the vectors are unit vectors, and in the infinite-dimensional case, we would take the closure of such states in the trace norm. We can interpret as representing an ensemble where is the proportion of the ensemble whose states are formula_23. When a mixed state has rank 1, it therefore describes a 'pure ensemble'. When there is less than total information about the state of a quantum system we need density matrices to represent the state.


title: Quantum entanglement

text: Experimentally, a mixed ensemble might be realized as follows. Consider a "black box" apparatus that spits electrons towards an observer. The electrons' Hilbert spaces are identical. The apparatus might produce electrons that are all in the same state; in this case, the electrons received by the observer are then a pure ensemble. However, the apparatus could produce electrons in different states. For example, it could produce two populations of electrons: one with state formula_24 with spins aligned in the positive direction, and the other with state formula_25 with spins aligned in the negative direction. Generally, this is a mixed ensemble, as there can be any number of populations, each corresponding to a different state.


title: Quantum entanglement

text: Following the definition above, for a bipartite composite system, mixed states are just density matrices on . That is, it has the general form


title: Quantum entanglement

text: where the "w" are positively valued probabilities, formula_27, and the vectors are unit vectors. This is self-adjoint and positive and has trace 1.


title: Quantum entanglement

text: Extending the definition of separability from the pure case, we say that a mixed state is separable if it can be written as


title: Quantum entanglement

text: where the are positively valued probabilities and the formula_29's and formula_30's are themselves mixed states (density operators) on the subsystems and respectively. In other words, a state is separable if it is a probability distribution over uncorrelated states, or product states. By writing the density matrices as sums of pure ensembles and expanding, we may assume without loss of generality that formula_29 and formula_30 are themselves pure ensembles. A state is then said to be entangled if it is not separable.


title: Quantum entanglement

text: In general, finding out whether or not a mixed state is entangled is considered difficult. The general bipartite case has been shown to be NP-hard. For the and cases, a necessary and sufficient criterion for separability is given by the famous Positive Partial Transpose (PPT) condition.


title: Quantum entanglement

text: The idea of a reduced density matrix was introduced by Paul Dirac in 1930. Consider as above systems and each with a Hilbert space . Let the state of the composite system be


title: Quantum entanglement

text: As indicated above, in general there is no way to associate a pure state to the component system . However, it still is possible to associate a density matrix. Let


title: Quantum entanglement

text: which is the projection operator onto this state. The state of is the partial trace of over the basis of system :


title: Quantum entanglement

text: The sum occurs over formula_36 and formula_37 the identity operator in formula_38. is sometimes called the reduced density matrix of on subsystem . Colloquially, we "trace out" system to obtain the reduced density matrix on .


title: Quantum entanglement

text: This demonstrates that, as expected, the reduced density matrix for an entangled pure ensemble is a mixed ensemble. Also not surprisingly, the density matrix of for the pure product state formula_41 discussed above is


title: Quantum entanglement

text: In general, a bipartite pure state ρ is entangled if and only if its reduced states are mixed rather than pure.


title: Quantum entanglement

text: Reduced density matrices were explicitly calculated in different spin chains with unique ground state. An example is the one-dimensional AKLT spin chain: the ground state can be divided into a block and an environment. The reduced density matrix of the block is proportional to a projector to a degenerate ground state of another Hamiltonian.


title: Quantum entanglement

text: The reduced density matrix also was evaluated for XY spin chains, where it has full rank. It was proved that in the thermodynamic limit, the spectrum of the reduced density matrix of a large block of spins is an exact geometric sequence in this case.