in general , the certification of _ entanglement _ requires to perform specific measurements on the quantum state one is willing to test . experimentally , this is a delicate task since mismatches between either the state or the measurements and their actual physical implementation may lead to false - positive conclusions about the presence of entanglement in the network .although such mismatches can in principle be patched in experimental setups , the situation becomes dramatic when considering applications , where the devices used are not trusted as they could have been provided and controlled by some adversary .one solution to this problem is the use of _ device - independent _ techniques , for which no assumption is made on the devices that generate the state or perform the measurements . in this approachthe devices are seen as black boxes , accessed only with classical inputs ( corresponding to the measurement choices ) and providing classical outputs ( corresponding to the measurement outcomes ) .although such _ device - independent entanglement witnesses _ have been soundly considered in the past years , their physical implementation turns out to be very demanding for it requires one to observe a bell inequality violation without the presence of loopholes .a midpoint among the aforementioned cases is the _ semi - device independent _ approach , which relies on the presence of _ quantum steering _ to certify entanglement in the network .this is an asymmetric situation in the sense that only some of the parties in the network use trusted devices while others do not .this approach is less demanding experimentally than the device - independent case , but it still presents practical interest for adversarial situations ; for instance , one could think of a practical semi - device independent network composed by a single central trusted provider , while the remaing parties , the clients , hold untrusted devices . for these reasonsthe study of quantum steering has increased substantively in recent years .methods to certify all kinds of multipartite entanglement in semi - device independent networks were presented -and experimentally demonstrated- very recently in ref .these methods rely on _ semi - definite programming _( sdp ) techniques .they represent an important achievement for the certification of entanglement in quantum networks .in fact , these techniques certify entanglement in networks with amounts of noise that make them undetectable by the existing fully device - independent techniques .  herewe apply such semi - device independent entanglement certification techniques to the three - qubit w state .our motivation to consider the w state is two - fold .first , this state displays both genuine multipartite entanglement ( gme ) and entanglement in its reduced states , being then a flexible resource for the implementation of quantum networks .this is not the case for the ghz state implemented in ref . , as its reduced state is separable .second , it is not known whether the reduced state of the w state can violate any bell inequality , while here we show that it does present steering .  in this paperwe show that by sharing a w state , every party can detect all types of entanglement without the need of trusting the measurements that the other parties are performing .this puts the w state as a promising candidate to implement asymmetric cryptographic protocols .we demonstrate the feasibility of such aforementioned techniques for entanglement certification in a proof - of - principle photonic experiment .additionally , we use the recent methods for one - sided device independent randomness certification presented in ref . to estimate the amount of randomness that can be obtained in bipartitions of the w state .+ the paper is organized as follows . in sec .[ sec.witnesses ] we first provide a general overview on the construction of semi - device independent witnesses required for all types of entanglement .then , in sec .[ sec.theoretical ] we provide theoretical results for the witnesses values when a three - qubit w state is considered . in sec .[ sec.experimental ] we implement the witnesses in an optical experiment , and present the corresponding results .next , as an application , in sec .[ sec.rand ] we analyse the amount of one - sided randomness certified from bipartitions of the w state . finally , we present our conclusions in sec .[ sec.conclusion ] .in this section we first recall the methods of ref. to construct multipartite semi - device independent entanglement witnesses .the intuition is the following . assuming that the quantum state ( denoted by ) distributed in the network is separable according to some particular decomposition ( _ e.g _ fully separable , separable across any bipartition , etc . )imposes constraints on the collection of all possibly observable set of post - measured states that the untrusted parties create for the trusted ones . from these constraintsone can then determine if the original state could have the considered decomposition with sdp techniques in an efficient way .this sdp also provides experimentally friendly entanglement witnesses .   for illustrative purposes and simplicitywe narrow our focus to the distribution of among three parties , a , b and c , but it is worth noting that the witness constructions that will be presented can indeed be generalized for a larger number of parties .two semi - device independent cases arise ; namely , either one or two of the parties could be holding untrusted devices in the network . in the casewhere one party , say a , uses untrusted devices , it will be first interesting to analyze the reduced asymmetric network that stems between a and b when discarding the third party c ( top - left of fig .[ fig.fig1 ] ) .this corresponds to a bipartite steering scenario and the witness for such case will be derived in sec .[ sec.redent ] .note that the certification of entanglement in the reduced state shared by a and b guarantees the presence of entanglement across bipartitions a : bc and ac : b , regardless of whether c trusts his measurement device or not .  a slightly more complicated task is to certify tripartite entanglement when either one or two parties hold untrusted devices ( top - right and bottom of fig .[ fig.fig1 ] , respectively ) .equivalently , this task requires to decide whether the original state is fully separable or not , and we will construct the witness necessary to answer this question in sec . [ sec.fullent ] .next , the question will be extended for genuine multipartite entanglement ( gme ) in sec .[ sec.gme ] by asking if the state is biseparable .we start by analyzing the presence of entanglement in the reduced bipartite system left to a and b when c is disregarded ( see top - left in fig .[ fig.fig1 ] ) . in this casea and b are left with the quantum state  ] , and thus the collection known as a _ quantum assemblage _ , contains all the information obtainable in this measurement scenario . if is not entangled , it reads : where defines some probability distribution . in this case , the assemblage takes the form : with  ] , where denotes the number outcomes of a and and denote the dimension of a s and b s respective systems , we arrive at the following sdp test for bipartite entanglement with one untrusted party : where is the assemblage observed by b in this network . since , a sufficiently negative and large value of will always solve the second line of , and hence this sdp is strictly feasible .if we denote by the solution of for a fixed , then indicates that the decomposition can be found , and thus is separable . on the other hand ,if , some amount of identity noise has to be added to the assemblage to make it lhs , so we certify entanglement in .  furthermore , from the _ dual _ formulation of the _ primal _ problem , it is possible to define a set of operators , which are such that the linear functional : \label{eq.witness1unt}\ ] ] provides a strictly negative value only if demonstrates steering , certifying then the entanglement of . since the primal problem is strictly feasible , _ strong duality _holds , and the dual and primal solutions coincide .that is , .thus , constitutes the desired witness for bipartite entanglement with one untrusted party .  to conclude this section , note that the witness we have constructed here certifies entanglement between a and b , whether c is holding a device that is trusted or untrusted . in other words, this witness also certifies the presence of entanglement accross the bipartitions a : bc and b : ac , for any level of trust that c might have on his measurement device .we now move on to the full tripartite network , for which we wish to certify the presence of entanglement in the whole state distributed to a , b and c. the construction procedure is similar to the one from the previous section .if is fully separable , then :   we treat first the case in which only a uses an untrusted device , while b and c remain trusted ( see top - right of fig .[ fig.fig1 ] ) . in this case ,b and c are provided with the assemblage : , \label{eq.sigbcax}\ ] ] which , after using , takes the form : a decomposition of of the form can readily be seen to be similar to the one in , with the only difference that now the bipartite states of b and c conditioned on and are separable .this last requirement ( separability ) can not , in general , be translated to a finite number of linear matrix inequalities and positive constraints as before , because the set of separable states has a complicated structure .however , separability can be relaxed to _ positivity under partial transposition _ , which is now a valid sdp constraint -and equivalent to separability whenever the product of the dimensions of b and c satisfies .therefore , we define the relaxed set : where denotes the partial transposition operation with respect to system b. in the same fashion as in sec .[ sec.redent ] , with the help of the maximally mixed assemblage for b and c , namely  ] is the maximally mixed assemblage for c. the set of dual variables of program enable the construction of the witness : , \label{eq.witness2unt}\ ] ] which provides a strictly negative value if and only if demonstrates steering .   in this sectionwe move to the more delicate task of certifying genuine tripartite entanglement in the state shared by a , b and c. if is not genuinely tripartite entangled , it is biseparable and has the form : where , and are unnormalised probability distributions . for the case of one party using an untrusted device ( top - right of fig .[ fig.fig1 ] ) , using in leads to : the first summation term in has the same structure as the decomposition in , with the only difference that now may even be entangled .thus , the relevant set defined for this first decomposition term is : which clearly involves valid sdp constraints only .the second summation term in has two main features : _( i ) _ it does not demonstrate steering from a to b. this implies that tracing out c will leave b with an lhs assemblage with respect to a. _ ( ii ) _ it is separable across b : c .the first feature , having an lhs model , is readily translated to sdp constraints , as we have seen in the previous sections .the second one , separability , has to be relaxed to positivity under partial transposition , as explained in sec .[ sec.fullent ] .thus , the relaxed set corresponding to the second decomposition term is given by :  = \sum_{\mu } d_{\mu}(a|x)\sigma^{\text{b}}_{\mu},\right .\\ \ \left .\sigma^{\text{b}}_{\mu}\geq0,\ \left(\sigma^{\text{bc}}_{a|x}\right)^{t_{\text{b } } } \geq0 \right\}. \end{array } \label{eq.siggmesetbac}\ ] ] the third summation term of is identical to the second term , except that the roles of b and c are interchanged . from the previous claims we can now write explicitly the sdp test for genuine tripartite entanglement with one untrusted party : and the dual formulation of this problemprovides a witness , defined as in , such that certifies that is genuinely tripartite entangled .  for the case of two parties using untrusted devices ( bottom of fig .[ fig.fig1 ] ) , substituting in gives : the first summation term of the decomposition obtained in has only one main feature , that it may contain steering from b to c , but never from a to c. hence , it defines the set as : the second summation term appearing in has the same structure as the first one , and thus the set is straightforwardly defined in the same manner as in . the third term in , on the other hand , has two features : _( i ) _ it corresponds to an lhs assemblage , and _( ii ) _ the probability distribution is _ quantum _ , in the sense that it arises from local measurements performed on ( possibly entangled ) states .deciding if a probability distribution is quantum is not straightforward because the quantum set lacks of a precise characterization .nevertheless , it is possible to construct a hierarchy of well characterized sdp relaxations of the set , the so - called navascus - pironio - acn ( npa ) hierarchy .the npa hierarchy , originally introduced for probability distributions , can be generalized to assemblages , in the sense that one can define the -th relaxed set of assemblages for c encoding all the constraints on orthogonality and commutativity for the measurement operators of a and b ( see for more details ) .given the above , the relaxed set is : where we had to use the finite set of non - signalling strategies to decompose the quantum probability distribution in terms of a finite number of distributions ( deterministic strategies are insufficient here because of the existence of quantum correlations lying outside the local set ) .the sdp test for genuine tripartite entanglement with two untrusted parties is , therefore : and the corresponding semi - device independent witness is obtained from duality theory and has the same structure as .here we provide numerical values for the three - qubit w state and discuss the fact that parties a , b , and c can check for all kinds of entanglement without trusting the others , and certify one - sided randomness as well . in all that follows we consider that the measurements performed by all trusted boxes are pauli observables , namely , , and .our theoretical findings are summarized in the second column of table [ tab.1 ] .since the w state is symmetric , all reductions are equivalent regardless of the party that is discarded .specifically , , where denotes the two - qubit maximally entangled state .the reduced state turns out to be steerable with a theoretical violation of .this value is relatively small because of the detrimental contribution of the separable state .such violation not only guarantees the presence of entanglement in the reduced state , but it also certifies the presence of entanglement across any bipartition of the tripartite network , regardless of whether the third party ( the discarded one ) is using a trusted device or not , as explained in the first paragraph of sec .[ sec.scenarios ] .  for the tripartite w state, we observe the presence of entanglement and gme both in the `` one untrusted '' scenario and in the `` two untrusted '' scenario as well ( see lines 2 - 5 of table [ tab.1 ] ) .note that the violations for the `` one untrusted '' scenario are always better than for the `` two untrusted '' scenario , because in the former case there is more useful information available ( about the state ) than in the latter case .the values for tripartite entanglement are also always better than the values obtained for gme , as the presence of the latter implies the presence of the former , but the converse is not true in general ; that is , a state might be entangled without being gme .to demonstrate the practical utility of the theoretical results presented in sections [ sec.witnesses ] and [ sec.theoretical ] , we produced a three - qubit w state using photon pairs produced by spontaneous parametric down conversion ( spdc ) .figure [ fig : setup ] shows the experimental setup .two 1 mm thick type - i non - linear bbo crystals with optical axes oriented perpendicularly were pumped with a 325 nm continuous - wave hecd laser , producing degenerate photon pairs centered around 650 nm . using an additional half - wave plate in the path of photon 1 , the crossed - crystal arrangement produces two polarization entangled photons in the target state : qubits and were encoded in the polarization of the photons 1 and 2 , respectively .qubit was encoded in the path of photon 2 .initially , qubit is in the state . to produce the w state, we entangle the path and polarization degrees of freedom ( dof ) of photon 2 using a polarization - dependent mach - zehnder interferometer composed of two beam displacers ( bds ) and several half - wave plates ( hwps ) , as has been described in refs .the angles of the hwps are shown in figure [ fig : setup ] .we label the input and output paths ( 0 and 1 in the figure ) such that when the polarization state is , the output state is . for input vertical polarization ,the interferometer implements the transformation by controling the polarization of the pump laser , the initial polarization entangled state was prepared with and . renaming the polarization state and ,our setup produces a three - qubit state that is ideally a state .a set of 216 joint projective measurements in the , and pauli basis were performed on all three qubits , which allowed us to evaluate the sdp tests developed above . as an example ,[ fig : expresults ] shows the reconstructed density matrices of system ac when untrusted projects on different states . to perform projective measurements on qubit ( polarization of photon 1 ) , the usual system consisting of a quarter - wave plate ( qwp ) , hwp and a polarizing beam splitter ( pbs )is used . for projective measurements on qubit , a qwp , hwp and bd are used .this measurement system works in much the same way as that of qubit , however , after the projection on a given polarization state , the bd maps the state of the path dof at its input into the polarization dof at its output . in this fashion , the state describing the path dof , which is now encoded in the polarization dof , can be measured using the same arrangement as in photon 1 .the photons were spectrally filtered with 3 nm fwhm bandwidth filters centered at 650 nm ( not shown in the figure ) , coupled into single - mode optical fibers using microscope objectives and registered with single photon detectors and coincidence electronics ( the `` & '' box in fig .[ fig : setup ] ) .the methods described in sec . [ sec.witnesses ] were designed to detect entanglement and certify randomness from an observed _ physical _ assemblage . however , due to the unavoidable problem of finite statistics in any experiment , the assemblage that is experimentally observed does not satisfy the non - signalling property . to overcome this problem we took the following steps .first , we construct a physical assemblage that approximates the experimental data . this step is done with a least - squares optimization , an sdp program that minimizes the distance from the experimental assemblage to the set of physical assemblages bounded by the non - signalling constraints .the second step consists of using the constructed physical assemblage to obtain the desired witness , following the sdp techniques for entanglement detection .the last step is to apply the derived witness , which is simply a linear functional , to the experimental assemblage to show the presence of entanglement / randomness in the network .r c.1 cm c c.1cm l l  & & +  ' '' ''  ent . in reductions  & & + ent . _ ( 1 untrusted ) _ & & + ent . _ ( 2 untrusted ) _ & & + gme _ ( 1 untrusted ) _ & & + gme _ ( 2 untrusted ) _ & & +   our experimental results are summarized in the second column of table [ tab.1 ] .the error bars were calculated by performing monte carlo simulation ( 494 rounds ) assuming poissonian count statistics of our measurement results .experimentally , the reduced state is not entirely symmetric because of imperfections in the optical setup , such as temporal and spatial mode mismatch .thus , we analyzed all reductions and found that the highest violation of is obtained when discarding party , corresponding to to the polarization of photon 1 .this is due to the fact that the entanglement that survives , between qubits and , is encoded entirely in the polarization and spatial qubits of photon 2 .as far as the experimental certification of tripartite entanglement and genuine multipartite entanglement ( gme ) are concerned , the corresponding observed witness values are shown in lines 2 - 3 and 4 - 5 of table [ tab.1 ] , respectively .one obtains a negative value ( violation ) for these two types of tripartite entanglement , both in the `` one untrusted '' and in the `` two untrusted '' scenarios .the experimental values are systematically smaller than the theoretical ones , except in one case .this is expected since the experimental state is not perfectly pure .the case where the measured value agrees with the theory within the error interval corresponds to the situation where the correlations between two internal degrees of freedom of the same photon ( path and polarization ) are the most relevant . in this special casethe purity of the reduced state can be very high experimentally .even with these small discrepancies between theory and experiment , we successfully certify the presence of entanglement and gme in the considered semi - device independent networks .one of the most interesting applications following the semi - device - independent quantum information approach is the _ semi - device independent random number generation _ . to carry out this task, one must bound the predictability of the outcomes of the black boxes ( parties holding untrusted devices ) , only from the observation of a certain assemblage by the parties holding trusted devices in the network . just as in the previous sections ,the black boxes might be provided with any _ a priori _ unknown quantum state , but now may even be correlated with some other quantum system in the possession of a malicious eavesdropper e , such that \sum_{e}\sigma^e = \sigma\sum_{r}\sigma_{r|m}^e = \sum_{r}\sigma_{r|m'}^e\ \ \forall e , m , m'\sigma^e_{r|m}\geq 0 \ \ \ \forall r , m , e ] to re - express the objective function in the first line of . intuitively , eve may prepare any convex combination of the unnormalized assemblages , which are such that , whenever eve obtains the result after measuring her system , she then guesses that the outcome of the black boxes was . thus , eve needs as many preparations as possible values that can take , and would be the assemblage obtained if the information of eve s outcome were available .the first constraint in translates the fact that eve has to reproduce on average the observed assemblage , since otherwise her attack would be detected by the party holding the trusted device .the second and third constraints , non - signalling and positivity respectively , guarantee that the assemblages prepared by eve stem from quantum theory . in fact , any bipartite non - signalling assemblage admits a quantum realization .  once again , duality theory allows us here -from the dual formulation of - to obtain a steering inequality ( _ i.e. _ a linear functional ) acting on the set of assemblages of c , having the same structure as , and such that . finally , assuming independent and identically distributed ( iid ) rounds in the experiment , the amount of genuine random bits certified is given by , the _ min - entropy _ of the semi - device independent guessing probability .note that , when no random bits can be certified ( ) , as e guesses with probability 1 the outcome of the boxes and thus there is no unpredictability . on the other hand , any value , guarantees unpredictability and hence provides a strictly positive amount of randomness .we first analyzed the reduced state of the three - qubit w state .though we found that the state is steerable ( as shown in the first line of table [ tab.1 ] ) , it is not possible to extract one - sided genuine randomness from such reduced state with the measurements considered here . on the other hand ,one - sided randomness certification turns out to be appealing when bipartitions of the tripartite w state are considered .in fact , when two of the boxes are seen as a single untrusted measurement performed on some unknown quantum state , while the other qubit , c , remains trusted ( see fig .[ fig.fig2 ] ) , we manage to certify random bits from the outcome of the measurement corresponding to the observables and acting on the two - qubit subspace reduction of the w state .the fact that no one - sided genuine randomness could be extracted from the reduced state of the three - qubit w state is unfortunate but interesting .this is analogous to a similar phenomenon , known as _ bound randomness _ , which arises in the fully device independent scenario where the two parties hold untrusted devices .more precisely , in the fully device independent scenario , bound randomness arises in nonlocal correlations for which a non - signalling eavesdropper can find out a posteriori the result of any implemented measurement .thus , the fact that any reduction of the w state is steerable but does not allow for one - sided randomness certification , may tentatively be refered to as _ one - sided bound randomness _ : a form of steerable correlations for which an eavesdropper can predict the result of any of the measurements performed on the untrusted side .   the scenario presented in fig .[ fig.fig2 ] turns out to be relevant and well suited for our experimental implementation of the photonic w state ( see sec .[ sec.experimental ] ) , as a physical bipartition of the state stems between the two photons produced . in this sense, it is natural to consider the photon encoding both polarization and path qubits as a single party , and analyze the amount of randomness of the outcomes retrieved when untrusted measurements are performed on such physical part of the system .first of all , we checked that the experimental data of each of the the reduced states does not reveal any amount of one - sided randomness , as predicted by the theory .subsequently , we managed to certify bits from the bipartitions of the w state .this value falls far from the theoretical value of bits .this discrepancy is due to the fact that the amount of randomness is extremely sensitive to the visibility of the pure state with respect to white noise .for instance , we observe that for the number of one - sided random bits that can be certified is already less than unity .the obtained theoretical results are nevertheless encouraging for the near future , as sources with better visibilites should allow to certify higher and higher amounts of genuine random bits .in conclusion , we show that a recently introduced method for certification of entanglement when semi - device independent measurements realized in a quantum network can be successfully employed for the case where a w state is distributed .we study in detail the case of a tripartite configuration , even though the method is valid for larger networks .entanglement is witnessed for a few illustrative combinations of trusted and untrusted parties .we also present experimental results obtained with a proof of principle optical set - up .we observe good qualitative agreement between theory and experimental results , and verify the strong dependence of the witnessed entanglement on the degree of purity of the initial state .we further investigate the certification of genuine randomness .we observe that one - sided randomness can not be certified .however , considering bipartitions of the tripartite w state and the bipartition with two elements untrusted , it is possible in principle to certify up to 1.58 random bits . analyzing the experimental implementation ,only random bits were certified .this discrepancy between the expected and measured values emphasizes the critical dependence of the amount of random information certified on the purity of the initial state .our results promote the w state as a key candidate for the implementation of device semi independent protocols , where some of the parties use untrusted devices .we thank o. jimenez - farias for discussions . this work was supported by the mexican conacyt graduate fellowship program , the ramon y cajal fellowship , spanish mineco ( severo ochoa grant sev-2015 - 0522 and foqus ) , the axa chair in quantum information science , the generalitat de catalunya ( sgr875 ) , fundacio privada cellex , erc cog qitbox and the erc adg nlst .financial support was also provided by brazilian agencies faperj , cnpq , capes , and the national institute of science and technology for quantum information .the dual formulation of the semi - definite programs presented in the main text provide a set of witness operators ( for the case where only a holds an untrusted device ) and ( for the case where both a and b hold untrusted devices ) which constitute semi - device independent witnesses of entanglement and of one - sided genuine randomness of the form : \geq 0 ] .note that it is possible to write these witnesses in a friendlier form . by introducing the observables for a and for b in the previous two expressions , and by expanding the resulting matrices in the complete basis of pauli operators where , , and , we obtain , respectively :   and = \sum_{xyz } f_{xyz } \langle a_xb_y\sigma^z \rangle , \label{eq.friend2unt}\ ] ] where denotes the expectation value of observables for a , for b and for c in the previous two expressions . in table table[ table.2 ] we provide numeric values for the coefficients defining theoretic and experimental semi - device independent witnesses of entanglement and one - sided genuine randomness .& & & & & & & & & & & & & & & & & & + & & 1 & 1 & & 1 & 1 & & 1 & 1 & & 1 & 1 & & 1 & 1 & & 842.54 & 4.730 + & & 0 & 0.006 & & 0 & -0.018 & & 0 & 0.021 & & 0 & -0.016 & & 0 & 0.003 & & 0 & 0 + & & 0 & -0.052 & & 0 & -0.020 & & 0 & -0.022 & & 0 & -0.060 & & 0 & -0.016 & & 0 & -0.500 + & & -0.547 & -0.411 & & 0.062 & -0.006 & & 0.317 & 0.368 & & 0.440 & 0.435 & & 0.252 & 0.073 & & -14.71 & 0.670 + & & 0 & 0.011 & & 0 & 0 & & 0 & -0.008 & & 0 & 0.042 & & 0 & -0.036 & & 0 & -0.114 + & & -0.496 & 0.410 & & -0.006 & 0 & & 0 & -0.203 & & 0 & 0.242 & & 0 & -0.006 & & -138.75 & -0.070 + & & 0 & 0.094 & & 0 & 0 & & -0.274 & 0.004 & & -0.253 & -0.054 & & -0.111 & 0.059 & & 0 & 0.081 + & & 0 & 0.013 & & 0 & 0 & & 0 & -0.046 & & 0 & 0.062 & & 0 & -0.023 & & 0 & -0.091 + & & 0 & -0.020 & & 0 & 0 & & 0 & -0.015 & & 0 & -0.038 & & 0 & -0.225 & & 0 & -0.274 + & & 0 & -0.091 & & 0 & 0 & & -0.274 & 0.002 & & -0.253 & 0.055 & & -0.111 & 0.006 & & 0 & -0.025 + & & -0.496 & 0.398 & & -0.006 & 0 & & 0 & 0.196 & & 0 & 0.244 & & 0 & 0.013 & & -140.39 & 0.435 + & & 0 & 0.026 & & 0 & 0 & & 0 & 0.031 & & 0 & -0.014 & & 0 & 0.048 & & 0 & 0.287 + & & -0.299 & -0.411 & & 0.752 & 1 & & -0.022 & -0.022 & & 0.242 & 0.269 & & 0.352 & 0.440 & & -243.41 & -1.931 + & & 0 & 0.013 & & 0 & -0.018 & & 0 & -0.043 & & 0 & -0.021 & & 0 & 0.013 & & 0 & -0.066 + & & 0 & -0.001 & & 0 & -0.020 & & 0 & -0.017 & & 0 & -0.011 & & 0 & -0.001 & & 0 & 0.193 + & & 0.547 & 0.617 & & 0.055 & -0.006 & & 0.317 & 0.244 & & 0.185 & 0.223 & & 0.130 & 0.147 & & 126.65 & 0.599 + & & 0 & 0 & & 0 & 0.021 & & 0 & -0.037 & & 0 & 0.106 & & 0 & 0.004 & & 0 & 0.670 + & & 0 & 0 & & -0.839 & -0.982 & & 0.079 & -0.058 & & -0.157 & -0.131 & & -0.194 & 0.214 & & 0.355 & -0.149 + & & 0 & 0 & & 0 & -0.177 & & 0 & 0.013 & & 0 & -0.038 & & 0 & -0.010 & & 0 & 0 + & & 0 & 0 & & 0 & 0.069 & & 0 & 0.005 & & 0 & 0.078 & & 0 & 0.017 & & 0 & 0.139 + & & 0 & 0 & & -0.006 & 0 & & 0 & 0.275 & & 0 & 0.215 & & 0 & 0 & & -166.65 & -0.091 + & & 0 & 0 & & 0 & 0 & & 0 & 0.021 & & 0 & 0.016 & & 0 & 0.007 & & 0 & 0.760 + & & 0 & 0 & & 0 & 0 & & 0 & -0.010 & & 0 & -0.012 & & 0 & 0.004 & & 0 & 0 + & & 0 & 0 & & -0.172 & 0 & & 0 & 0.332 & & 0 & 0.205 & & 0 & 0.201 & & -67.07 & -0.303 + & & 0 & 0 & & 0 & 0 & & -0.274 & 0.079 & & -0.253 & 0.073 & & -0.111 & 0.007 & & 0 & 0.287 + & & 0 & 0 & & 0 & 0 & & 0 & 0.008 & & 0 & 0.024 & & 0 & 0.014 & & 0 & 0.174 + & & 0 & 0 & & 0 & 0 & & 0 & -0.064 & & 0 & 0.010 & & 0 & -0.015 & & 0 & 0 + & & 0 & 0 & & 0 & 0 & & -0.296 & 0.110 & & -0.253 & 0.087 & & -0.230 & 0.024 & & 0 & -0.168 + & & 0 & 0 & & 0 & 0.021 & & 0 & 0.021 & & 0 & 0.032 & & 0 & 0.013 & & 0 & 0.599 + & & 0 & 0 & & -0.891 & -0.982 & & -0.176 & 0.188 & & -0.157 & -0.166 & & -0.159 & 0.059 & & -62.88 & 0.076 + & & 0 & 0 & & 0 & -0.177 & & 0 & -0.068 & & 0 & -0.023 & & 0 & -0.035 & & 0 & 0 + & & 0 & 0 & & 0 & 0.069 & & 0 & -0.012 & & 0 & 0.021 & & 0 & 0.033 & & 0 & -0.066 + & & 0 & 0 & & 0 & 0.017 & & 0 & -0.003 & & 0 & -0.026 & & 0 & 0.013 & & 0 & 0.025 + & & 0 & 0 & & 0 & 0.159 & & 0 & 0.013 & & 0 & 0.026 & & 0 & -0.011 & & 0 & -0.131 + & & 0 & 0 & & -0.839 & -0.966 & & 0.079 & 0.056 & & -0.157 & -0.144 & & -0.194 & -0.325 & & -0.488 & 0 + & & 0 & 0 & & 0 & -0.202 & & 0 & 0.006 & & 0 & -0.035 & & 0 & -0.157 & & 0 & -0.001 + & & 0 & 0 & & 0 & 0 & & -0.274 & -0.074 & & -0.253 & -0.072 & & -0.111 & -0.060 & & 0 & 0.245 + & & 0 & 0 & & 0 & 0 & & 0 & 0.009 & & 0 & -0.012 & & 0 & 0.008 & & 0 & -0.081 + & & 0 & 0 & & 0 & 0 & & 0 & 0.048 & & 0 & 0.009 & & 0 & 0.053 & & 0 & 0 + & & 0 & 0 & & 0 & 0 & & -0.296 & -0.103 & & -0.253 & -0.087 & & -0.230 & -0.015 & & 0 & 0.070 + & & 0 & 0 & & -0.006 & 0 & & 0 & 0.261 & & 0 & 0.229 & & 0 & -0.009 & & -140.39 & 0.128 + & & 0 & 0 & & 0 & 0 & & 0 & -0.015 & & 0 & -0.002 & & 0 & -0.014 & & 0 & 0.105 + & & 0 & 0 & & 0 & 0 & & 0 & -0.014 & & 0 & -0.010 & & 0 & 0.120 & & 0 & 0 + & & 0 & 0 & & -0.172 & 0 & & 0 & 0.316 & & 0 & 0.227 & & 0 & 0.255 & & -39.89 & -0.041 + & & 0 & 0 & & 0 & 0.017 & & 0 & -0.014 & & 0 & 0.020 & & 0 & 0.001 & & 0 & -0.017 + & & 0 & 0 & & 0 & 0.159 & & 0 & -0.073 & & 0 & 0.021 & & 0 & -0.034 & & 0 & 0.149 + & & 0 & 0 & & -0.891 & -0.966 & & -0.176 & -0.162 & & -0.157 & -0.164 & & -0.159 & -0.135 & & -64.86 & -0.073 + & & 0 & 0 & & 0 & -0.202 & & 0 & -0.052 & & 0 & 0.007 & & 0 & -0.159 & & 0 & -0.056 + & & 0 & 0 & & 0.062 & -0.004 & & 0.317 & 0.236 & & 0.440 & 0.498 & & 0.252 & 0.073 & & -19.22 & -0.062 + & & 0 & 0 & & 0 & 0.103 & & 0 & -0.013 & & 0 & -0.004 & & 0 & 0.017 & & 0 & -0.132 + & & 0 & 0 & & 0 & -0.187 & & 0 & 0.001 & & 0 & -0.056 & & 0 & -0.157 & & 0 & -0.066+ & & 0 & 0 & & 0.841 & 0.977 & & -0.011 & -0.013 & & -0.004 & 0.059 & & 0.228 & 0.448 & & 17.26 & -0.801 + & & 0 & 0 & & 0 & 0 & & 0 & -0.023 & & 0 & -0.006 & & 0 & -0.023 & & 0 & 0.022 + & & 0 & 0 & & -0.172 & 0 & & 0 & -0.292 & & 0 & 0.241 & & 0 & -0.201 & & -39.18 & -0.056 + & & 0 & 0 & & 0 & 0 & & -0.296 & 0.004 & & -0.253 & -0.034 & & -0.230 & -0.014 & & 0 & 0.008 + & & 0 & 0 & & 0 & 0 & & 0 & -0.017 & & 0 & 0.014 & & 0 & 0.009 & & 0 & -0.021 + & & 0 & 0 & & 0 & 0 & & 0 & 0.026 & & 0 & -0.029 & & 0 & 0.048 & & 0 & 0.365 + & & 0 & 0 & & 0 & 0 & & -0.296 & 0 & & -0.253 & 0.046 & & -0.230 & -0.023 & & 0 & -0.013 + & & 0 & 0 & & -0.172 & 0 & & 0 & 0.259 & & 0 & 0.247 & & 0 & 0.255 & & -39.90 & 0.004 + & & 0 & 0 & & 0 & 0 & & 0 & 0.057 & & 0 & -0.005 & & 0 & -0.116 & & 0 & 0.189 + & & 0 & 0 & & 0.055 & -0.004 & & 0.317 & 0.344 & & 0.185 & 0.221 & & 0.130 & 0.148 & & 103.36 & 1.202 + & & 0 & 0 & & 0 & 0.103 & & 0 & 0.001 & & 0 & -0.004 & & 0 & -0.033 & & 0 & 0.066 + & & 0 & 0 & & 0 & -0.187 & & 0 & -0.040 & & 0 & -0.006 & & 0 & -0.159 & & 0 & 0.065 + & & 0 & 0 & & 0.893 & 0.977 & & 0.500 & 0.516 & & 0.242 & 0.271 & & 0.223 & 0.254 & & 66.80 & 1.982 +   31ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1'''' [ 0]secondoftwosanitize [ 0 ] + 12$12 & 12#1212_12%12[1][0] * * ,  ( ) link:\doibase 10.1103/revmodphys.81.865 [ * * ,  ( ) ] \doibase http://dx.doi.org/10.1016/j.physrep.2009.02.004 [ * * ,  ( ) ] link:\doibase 10.1103/physreva.86.062325 [ * * , ( ) ] link:\doibase  10.1103/revmodphys.86.419 [ * * ,  ( ) ] link:\doibase  10.1103/physrevlett.98.230501 [ * * ,  ( ) ] link:\doibase 10.1103/physrevlett.106.250404 [ * * ,  ( ) ] link:\doibase 10.1038/nphys2705 [ * * , ( ) ] http://dx.doi.org/10.1038/ncomms1348 [ * * ( ) ] link:\doibase 10.1038/nature15759 [ * * ,  ( ) ] link:\doibase  10.1103/physrevlett.115.250402 [ * * ,  ( ) ] link:\doibase  10.1103/physrevlett.115.250401 [ * * ,  ( ) ] link:\doibase 10.1103/physrevlett.98.140402 [ * * , ( ) ] link:\doibase 10.1038/ncomms8941 [ * * ( ) , 10.1038/ncomms8941 ] http://arxiv.org/abs/1604.00501 [ ( ) ] link:\doibase 10.1103/physreva.91.022101 [ * * ,  ( ) ] link:\doibase  10.1103/physreva.91.032108 [ * * ,  ( ) ] http://stacks.iop.org/1367-2630/17/i=11/a=113010 [ * * ,  ( ) ] _ _ ( , , ) link:\doibase 10.1103/physrevlett.98.010401 [ * * ,  ( ) ] http://stacks.iop.org/1367-2630/10/i=7/a=073013 [ * * ,  ( ) ] * * ,  ( ) link:\doibase 10.1103/physrevlett.109.150403 [ * * ,  ( ) ] link:\doibase 10.1103/physrevlett.113.240501 [ * * ,  ( ) ] http://stacks.iop.org/1751-8121/47/i=42/a=424028 [ * * ,  ( ) ] link:\doibase 10.1103/physreva.85.010301 [ * * ,  ( ) ] link:\doibase 10.1088/1367 - 2630/16/1/013035 [ * * ( ) , 10.1088/1367 - 2630/16/1/013035 ] \doibase http://dx.doi.org/10.1016/0375-9601(93)90880-9 [ * * ,  ( ) ] link:\doibase  10.1103/physrevlett.115.190403 [ * * ,  ( ) ] http://arxiv.org/abs/1505.00053 [ ( ) ]

Abstract: recently [ cavalcanti _ et al . _ nat commun * 6 * , 7941 ( 2015 ) ] proposed a method to certify the presence of entanglement in asymmetric networks , where some users do not have control over the measurements they are performing . such asymmetry naturally emerges in realistic situtations , such as in cryptographic protocols over quantum networks . here we implement such `` semi - device independent '' techniques to experimentally witness all types of entanglement on a three - qubit photonic w state . furthermore we analise the amount of genuine randomness that can be certified in this scenario from any bipartition of the three - qubit w state .


cloud computing is developed based on various recent advancements in virtualization , grid computing , web computing , utility computing and related technologies .cloud computing provides both platforms and applications on demand through the internet or intranet .some of the key benefits of cloud computing include the hiding and abstraction of complexity , virtualized resources and efficient use of distributed resources . some examples of emerging cloud computing platforms are google app engine , ibm blue cloud , amazon ec2 , and microsoft azure .cloud computing allows the sharing , allocation and aggregation of software , computational and storage network resources on demand .cloud computing is still considered in its infancy as there are many challenging issues to be resolved .youseff et al . establish a detailed ontology of dissecting cloud into five main layers from top to down : cloud application ( saas ) , cloud software environment ( paas ) , cloud software infrastructure ( iaas ) , software kernel and hardware ( haas ) , and illustrate their interrelations as well as their inter - dependency on preceding technologies .cloud data center can be a distributed network in structure , which is composed of many computing nodes ( such as servers ) , storage nodes , and network devices .each node is formed by a series of resources such as cpu , memory , network bandwidth and so on .each resource has its corresponding properties .there are many different types of resources for cloud providers . the definition and model defined by this paperare aimed to be general enough to be used by a variety of cloud providers . in this paper , we focus on infrastructure as a service ( iaas ) in cloud data centers .  in a traditional data center ,applications are tied to specific physical servers that are often over - provisioned to deal with workload surges and unexpected failures .such configuration rigidity makes data centers expensive to maintain with wasted energy and floor space , low resource utilizations and significant management overheads . with virtualization technology ,today s cloud data centers become more flexible , secure and on - demand allocating .one key technology plays an important role in cloud data center is resource scheduling .one of the challenging scheduling problems in cloud data center is to consider allocation and migration of reconfigurable virtual machines and integrated features of hosting physical machines .it is extremely difficult to research widely for all these problems in real platforms because the application developers ca nt control and process network environment .what is more , the network conditions can not be predicted or controlled .the research of dynamic and large - scale distributed environment can be achieved by building data center simulation system , which supports visualized modeling and simulation in large - scale applications in cloud infrastructure .data center simulation system can describe the application workload statement , which includes user information , data center position , the amount of users and data centers , and the amount of resources in each data center . using this information , data center simulation system generates requests and allocates these requests to virtual machines .  by using data center simulation system , application developers can evaluate suitable strategies such as distributing reasonable data center resources , selecting data center to match special requirements , improving resource utilization and load balancing , reducing total energy - consumptions , reducing costs and so on .we will look at some closely related work firstly .there is quite intensive research conducted for cloud simulators . in this paper , we concentrate on open - source simulators which we can easier access .dumitrescu and foster introduce gangsim tool for grid scheduling .buyya et al .introduce gridsim toolkit for modeling and simulation of distributed resource management for grid computing .calheiros et al . introduce modeling and simulations of cloud computing environments at application level , a few simple scheduling algorithms such as time - shared and space - shared are discussed and compared .sakellari et al . complement a survey of mathematical models , simulation approaches and testbeds in cloud computing , which aims to enable researcher to find suitable modelling approach and simulation implementation .ikram et al . introduce a novel cloud resource management service model and its simulation - based evaluations are mainly focusing on two applications dynamic service composition .nuu et al . propose a scheme for modeling and experimenting combined smart sleep and power scaling algorithms in energy - aware data center networks .gurout et al . provide a survey on energy - aware simulation techniques with dvfs ( dynamic voltage and frequency scaling ) .cloudanalyst aims to achieve the optimal scheduling among user groups and data centers based on the current configuration .both cloudsim and cloudanalyst are based on simjava and gridsim , which treat a cloud data center as a large resource pool and consider application - level workloads .kliazovich et al . propose an energy - aware simulation environment named greencloud for cloud datacenters at package level .nunez et al . introduce a new simulator of cloud infrastructure named icancloud using c++ and compare the performance with cloudsim .tian et al . propose cloudsched , a novel lightweight simulation tool for vm scheduling with lifecycle in cloud data centers .cloud simulators can be divided into various categories according to their features . in this section, we will give a brief comparison with different categories by extending the comparison category in [ 9 ] .the open - source simulators are selected because we can study their source codes in details , develop new algorithms and improve them if necessary .the four open source simulators , namely cloudsim , icancloud , greencloud , cloudsched , are representative of many related simulators because we study the architecture design , modeling elements , simulation process , performance metrics and scalability .these simulators have common features such as in architecture , modeling elements , simulation process as well as their own characteristics such as focusing on different service layers and with different performance metrics .cloudsim is well known simulator for cloud computing , it can be extended easily but currently it does not consider parallel experiments or lifecycles of vms .the icancloud implements parallel experiments but does not consider energy consumption or vm migration .greencloud models detailed energy consumptions for different physical components .cloudsched can model lifecycle of requests , and provide different metrics for load - balance , energy efficiency and utilization etc .four open source cloud data centers simulators ( cloudsim , greencloud , icancloud , cloudsched ) are compared together in table 1 .  [cols="<,<,<,<,<",options="header " , ]   +in this section , we will discuss the performance comparison of icancloud and cloudsim , cloudsched and cloudsched with a focus on the scalability .we also compare the typical outputs of all compared simulators .    in the comparison between icancloud and cloudsim , jobs in cloudsimare modeled by configuring input size , processing length and output size .the jobs in the simulation experiments have 5 mb input size , 30 mb output size , 1,200,000 mi processing length .in addition , jobs would take advantage of all the available cpu capacity on vms and the vms they used are 9,500 mips .of course , a new application model is developed in icancloud to execute the same functionality as cloudsim .the experimental environment is on a computer with a cpu core i3 and 4 gb of ram memory .6(a ) demonstrates the execution time comparison of cloudsim and icancloud , the x - axis presents the number of jobs executed in each experiment , y - axis presents the vms number and its type , and z - axis presents the time required to execute each experiment ( measured in seconds ) in log - scale .it s obvious that both simulators need more execution time when increasing the number of jobs , while these simulators would have different impact when increasing the vms number .when the vms number is more than 2500 , the execution time keeps stable in icancloud , while the execution time is influenced directly by both vms number and jobs number . in most experimental cases with jobsamount less or equal to 50000 , icancloud is faster than cloudsim , and in all tests with 250k jobs , icancloud is faster . under all tests , icancloud shows better performance in execution time than cloudsim .6(b ) presents the memory consumption comparison in each experiment for cloudsim and icancloud .it can be noticed in this graph that icancloud requires more memory than cloudsim .up to 1000 vms , the amount of memory required by both simulators is similar .when using more than 1000 vms , the amount of memory required by icancloud goes up much faster than cloudsim .  in general , icancloud is faster in large scale experiments and provides better scalability , but requires more memory than cloudsim .[ htp ! ]    in the comparison between cloudsim and cloudsched , the comparison is a bit complex than the comparison in section 7.1 , a new construct method is created with start - time and end - time parameters , which refers to the lifecycle of a request .the file size of request represents the required capacity of all requests .the start - time , end - time generation approaches are same , servers ( named vms in cloudsim ) and requests ( named cloudlet in cloudsim ) both adopt the ec2 specifications .list scheduling algorithm is implemented in both simulators , in which requests would be allocated to a pm with the lowest utilization . the experimental environment is based on a dell computer with a cpu core i5 and 8 gb of ram memory .[ htp ! ]   fig .7(a ) illustrates the time consumption of each experiment , where x - axis shows the requests number in each experiment for cloudsim and cloudsched , y - axis shows the number of pms and simulators they belong to , and z - axis shows the time required in millisecond unit to simulate each experiment .it is also apparently observed that larger number of requests and number of pms need more time in both simulators . when the number of vms is less than 10,000 , cloudsched always costs less time to complete simulation . as for the numbers of vmsare 50,000 and 25,000 , cloudsched takes less time than cloudsim , while cloudsched takes longer time when the number of pms is more than 5,000 . as the ratio of the number of vms to the number of pms increases , like 500,000 : 500, cloudsim shows its strength .note that the ratio of vms to pms may be varying from a few to a few tens in a real cloud data center .7(b ) shows the memory consumption comparison of each simulation in cloudsim and cloudsched . in cases when the vms number is relative small , like from 1,000 to 10,000 .cloudsched needs a little more memory , several megabytes , to execute simulations .while as the requests number becomes larger , cloudsched costs much less memory than cloudsim , the large difference happens when the request number is 500,000 .the reason is that the vm and pm model in cloudsched is simpler than the models in cloudsim .  in general ,cloudsched costs less time when the ratio of the number of vm requests to the number of pms is not too large ( like below 100 ) and costs much less memory than cloudsim .[ htp ! ]  in fig .8 , we compare the performance of four energy - conscious resource management strategies against a benchmark technique npa ( nonpoweraware ) . in the benchmark technique, the processors can be operated at higher possible processing capacity as 100% and do not consider energy - optimization during provisioning of vms to hosts .the first energy - conscious strategy for comparison is dvfs enabled , which means that the vms are resized during the simulation based on the dynamics of cpu utilization of the host .the other strategies are extensions of dvfs policy : mu ( minimum utilization ) strategy allocates vms on the minimal utilization nodes ; rs ( random selection ) strategy randomly allocates vms to hosts ; mc ( maximum correlation ) strategy allocates vms on the maximal correlation hosts .all these extensive strategies enable the idle nodes into sleep mode to save total energy and live migration of vms every 5s for adapting to the allocation .vms can be migrated to another host , if this operation will reduce energy consumption . in our simulation , the requests come randomly and we vary the number of hosts and vms to obtain data for the energy consumption and the number of migrations . from our simulations ,mc strategy shows the best energy - efficient effects as shown in fig .8 ( b ) . as for the number of migrations , npa and dvfs bothhave no migrations , while in other three strategies , mc strategy takes least number of migration in most cases .the data shown in figure 8 is the average of 5 times of repeated simulation .[ htp ! ]  in fig.9 with greencloud simulations , we collect the total energy consumption under variable data center load ( varying from 0.0 , 0.3 , 0.6 to 1.0 ) and variable number of servers ( varying from 100 to 400 ) both for dvfs only and dns+dvfs power management schemes .the x - axis formats like ( 100 , 0.0 ) represents the tests with 100 servers and 0.0 load , and ( 400 , 1.0 ) shows tests with 400 servers and 1.0 load . in our simulations , we set the type of workloads as hpc ( high performance computation ) and the results gathered are averaged over 5 runs with the random number generator . from the bar chart , generally , it s obvious that the total energy consumption increases as the number of servers increases .it also demonstrates that the dvfs scheme shows itself little sensitive to the input load of servers , while by contrast the dns+dvfs scheme shows precise sensitive to variable load .we also observe that under same number of servers and identical loads , the dns+dvfs scheme saves more energy than dvfs scheme .[ htp ! ]  in icancloud , fig .10 illustrates the results gathered by executing the model of phobos application along with the results of the same application implemented on icancloud .the figure represents the c / p metric for the experiments , where the small instance type recommended by amazon ec2 is provided , and the vms number and tracing intervals are varied . from the results , we can notice that in some cases , using the same size for the interval ( in years ) and increasing the vms number , causes an upward trend in the c / p metric .then , increasing the vms number provides the same execution time , which contributes to a increasing of the cost for this configuration . besides that, the mathematical model does not represent the time spent on performing i / o operations .because that there are still some problems for installation of current release of icancloud , we can not test more data but using results in its original publication .[ htp ! ]  in cloudsched , fig .11 shows average imbalance level of a cloud data center and five different scheduling algorithms for load balancing are compared .zhcj algorithm introduced in , zhjz algorithm , lif algorithm , rand algorithm , and round - robin ( round ) are compared . in these simulations ,different requests are generated as follows : the total numbers of arrivals ( requests ) can be randomly set ; all requests follow poisson arrival process and have exponential length distribution ; the maximum length of requests can be set ; for each set of inputs ( requests ) , simulations are run six times and all the results shown in this paper are the average of the six runs . in these simulations , the number of pms is fixed as 100 , the number of requests is varying from 250 to 1500 , and a pc with 2 ghz cpu , 2 gb memory is used for all simulations . from these simulations , we observe that lif algorithm outwits other four algorithms with average imbalance values , which shows that lif has a better load balance effects than others .in this paper , we mainly compare four open source simulators , namely cloudsim , greencloud , icancloud and cloudsched .these simulators can simulate the cloud data center scenarios from different layers in the cloud computing architecture . from their architectures , elements modeling , simulation process , performance metrics and outputs , we provide detailed comparisons about these simulators .considering the complexity of networks and the difficult to control the network traffics , simulators are crucial tools for research .we can see that none of them is perfect for all aspects and there are still much work to do to improve .one suggestion is to use different tools or their combinations for different optimization objectives such as load balance and energy - efficiency . for future work, there are still quite a few challenging issues for cloud simulating :  * * modeling different cloud layers*. as we compared in the paper , each tool may focus on one layer .currently there is still lack of tools that can model all cloud layers ( iaas , paas and saas ) . * * high extensibility*. when new policies and algorithms are added , modular design of the simulators can assure that new modules can be easily added , currently the four simulators still need improving this . * * easy to use and repeatable*. the simulators should enable users to set up simulation easily and quickly with easy to use graphical user interfaces and outputs .it can accept inputs from text files and output to text files ; can save simulation inputs and outputs so that modelers can repeat experiments , ensuring that repeated simulation yield identical results .* * considering user priority*. this is a real requirement .currently the four simulators do not consider this yet .different priority policies can be created for users to have different priorities for certain types of vms , so that more realistic scenarios can be considered . * * supporting multiple or federated data centers*. the simulator should be able to reflect and model the multiple or federated data centers in real world .cloudanalyst provides a framework by extending cloudsim and there is still much work to improve .this research is sponsored by the national natural science foundation of china ( nsfc ) ( grant number:61150110486 ) .99 a. beloglazov , j. abawajy , r. buyya , energy - 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Abstract: resource scheduling in infrastructure as a service ( iaas ) is one of the keys for large - scale cloud applications . extensive research on all issues in real environment is extremely difficult because it requires developers to consider network infrastructure and the environment , which may be beyond the control . in addition , the network conditions can not be controlled or predicted . performance evaluations of workload models and cloud provisioning algorithms in a repeatable manner under different configurations are difficult . therefore , simulators are developed . to understand and apply better the state - of - the - art of cloud computing simulators , and to improve them , we study four known open - source simulators . they are compared in terms of architecture , modeling elements , simulation process , performance metrics and scalability in performance . finally , a few challenging issues as future research trends are outlined .   cloud computing , data centers , simulators for cloud computing , resource scheduling


charles darwin explained the evolution of living organisms on the basis of the observation that only the species best adapted to their surroundings survive in a competitive environment .this idea , paraphrased as `` survival of the fittest '' , has since become the cornerstone of evolutionary theories .the idea has been refined over the years , and we now understand its genetic underpinnings .hereditary transmission of genetic information is not perfect , and occasional errors in dna replication produce mutations of living organisms .the mutated organism is in essentially the same environment as the original one , and both have to compete for the available resources .the resources are limited , and so the organism that can use them more efficiently obtains an edge over its competitors .the net result is that if the mutation improves the ability of the organism to survive , the mutated organism grows in number , otherwise it fades away . in this mechanism ,the mutations are not conscious adaptations .they occur randomly as a matter of fact most of them fail but once in a while they modify the organism in the right manner and improve the chances of its survival . if the intermediate steps are glossed over , the outcome looks like a solution to the optimisation problem , with the organisms adapting to the selection pressures exerted by the environment .all this is fairly logical , and can be illustrated by many examples ( see for instance ) .my aim here is to quantify this mechanism using a simple evolutionary model .more specifically , i consider the situation where a number of species are dependent on a common physical resource , say food .( this leaves out predator - prey conflicts where one species may become another s resource . )when the resource is available in plenty , there is hardly any competition , and all species prosper .the rate of growth of a species is then proportional to its population , and so all populations grow exponentially .this typically happens in the early stage of evolution of a new species .no resource is unlimited , however , even if it is continuously regenerated ( e.g. food availability ultimately depends on sunlight ) .a time comes when competition for the resource is inevitable . in the later stage of evolution , therefore , one species can prosper only at the expense of another , and eventually populations stabilise .  such a situation can be described by a set of linear evolution equations .( quad - ratic evolution equations are more appropriate in a predator - prey setting . )let the index label a set of coexisting species in a given environment , and let denote their populations at time .then the discrete time evolution of the populations can be written as a matrix equation ( generically is not symmetric ) , the fact that the next generation populations must arise from the present generation ones , even in case of mutations , makes this equation homogeneous .the diagonal terms represent the individual rates of growth , while the off - diagonal terms represent interactions between species . as mentioned above ,when the resource is available in plenty , the populations evolve according to : the interesting situation is the competitive stage , where the populations become interdependent due to mutual interactions and the nature of the interactions ( para - metrised by ) determines how they evolve .to analyse the competitive stage , let us choose normalisations such that a unit population of any species consumes the same amount of resource , and the total resource available at any time is one .then we have the conservation laws : the constraint on arises because the total population supported by a fixed resource is fixed . when applied to both sides of eq.(1 ) , it yields the constraint on as a consistency condition .the continuity of evolution in time implies that the matrix , describing the change in populations , clearly shows that what is gained by some species is lost by some others .obviously can take positive as well as negative values . as a matter of fact ,situations of both positive and negative interactions occur routinely in biological systems ( e.g. catalysis and inhibition , symbiosis and parasitic behaviour , defence mechanisms and cancer , etc . ) .situations of this type , where there is no net gain or loss , have been formally called zero sum games . in the conventional form of zero sum games , a multitude of strategiesare available to the players , and competition amongst the players leads them to choose a stable strategy .this stable strategy turns out to be a `` mini - max solution '' , i.e. each player chooses the strategy that maximises his minimum gain .no player can improve his performance by unilaterally departing from this stable strategy , and the explicit solution can be obtained by linear programming methods .the model described by eqs.(1 ) and ( 3 ) is somewhat different .first , in the evolutionary context , the strategies are not actively chosen but are created by random mutations . also competition for the resourceis guaranteed , because mutations produce closely related species in the same environment .it is then of importance to study the dynamics of the system to understand how the incorrect strategies are eliminated and the correct ones are selected .that requires not just the evaluation of the stable solution but also the manner in which it is approached .second , the quantitative gains and losses of various species depend not only on the choice of strategy but also on their current populations . in a sense, the more populous species gets more chances to grab the resources , and that alters the final outcome of the competition .let us first look at the simpler situation when .eqs.(1 ) and ( 3 ) then describe stochastic evolution of probability distributions , which has been extensively studied ( see for instance ) . the linear evolution is a markov chain , which in the generic case is ergodic and converges to a unique stationary distribution .( if the matrix has a block - diagonal structure , then each block can be studied independently . ) to see this , consider the asymptotic behaviour of as . at every iteration, is the weighted average of  with weights .the process of repeated averaging converges to the fixed point , with all rows identical , has only one non - vanishing eigenvalue , equal to one .it follows that has the leading eigenvalue corresponding to the stationary distribution , and remaining eigenvalues corresponding to transient distributions .the left and right eigenvectors for the leading eigenvalue are , the left and right eigenvectors satisfy the orthogonality relation , for .all transient distributions are orthogonal to and necessarily contain negative components .the next - to - leading eigenvalue provides the rate of convergence towards the stationary distribution , and can be obtained my maximising , with the vectors and orthogonal to and respectively , and .the convergence is monotonic because , .all these properties belong to altruistic evolution , since while . in the competitive case, some of the , and the consequences need to be analysed .the presence of both positive and negative contributions produces cancellations .monotonic convergence is no longer automatic ; oscillations and instabilities may occur in stead .an important restriction is imposed by the physical requirement that no population can become negative .( note that there is no such requirement on the components of the individual eigenvectors of . )the evolution must be modified whenever it drives some negative .the correct procedure is to stop the evolution at the instance becomes zero , eliminate row and column from the matrix , and then continue evolution in the reduced dimensional space .obviously , can be driven negative only if some is negative .the reduction of dimensionality , therefore , decreases the number of negative and increases the stability of the system .the inverse process , increasing dimensionality of the space , occurs when chance mutation creates a new species .it is known that even with , eq.(1 ) can not be evolved backward in time _indefinitely_. this is true in spite of the fact that generic stochastic matrices are positive definite and exists .if backward evolution is attempted , some is driven negative at some stage , and beyond that point interpretation of as populations ( or probabilities ) is lost .evolution further back in time is possible only by modifying .this is easy to see because eigenvalues of are the reciprocals of those for , and with , the growing transient distributions drive some out of their physically allowed range $ ] .it is useful to compare this evolution problem to quantum algorithms .both are constrained by conservation laws .while eq.(3 ) preserves the linear norm of the vector , quantum evolution preserves the quadratic norm .the most general evolution preserving the quadratic norm is described by orthogonal transformations for real variables , and by unitary transformations for complex variables .orthogonal transformations are generated by antisymmetric matrices ( generating matrices parametrise infinitesimal group transformations in the neighbourhood of identity ) , and they inevitably contain negative matrix elements the negative elements are an automatic consequence of the underlying conservation laws .( only orthogonal transformations without any negative matrix elements are simple permutation matrices . )although complete understanding of quantum evolution requires use of complex numbers , classical language extended to include negative probabilities can explain unusual features of certain simple systems ( e.g. quantum correlations of two spins violating bell s inequalities ) .recent developments in algorithms for quantum computation ( see for instance ) offer a hint of how evolution may change in presence of negative matrix elements .classical algorithms based on boolean logic can be expressed in terms of permutation matrices .quantum algorithms exploit two features to beat them , superposition of states ( which is a generic property of waves ) and quantum entanglement ( which is not relevant here ) .superposition means letting multiple states be in the same place at the same time , and it can reduce the spatial degrees of freedom required for the algorithm exponentially . cleverly designed destructive interference amongst superposed states can reduce the the time required to execute the algorithm by eliminating unwanted states .coexistence of species in biological evolution is not quite the same as superposition ; it allows simultaneous evolution of all species but without reducing the spatial degrees of freedom . but destructive interference is still an option available to reduce the evolution time .the known quantum algorithms reduce the execution time compared to their classical counterparts , at least by a constant factor if not polynomially or exponentially .it is important to note that biological evolution occurs over long time scales , and even a tiny change in the rate of growth fraction of a percent matters because that can translate into exponential changes in populations over a long time .the lessons learnt from quantum computation thus suggest that negative values of may create destructive interference and help the species reach their asymptotic populations faster , i.e. competition should beat altruism in picking a winner amongst the contenders .let us now explicitly analyse how evolution changes , when the range of is extended to include negative values .clearly , extending the range of can not make the evolutionary process any less powerful .the stationary eigenvalue of , , which follows just from the averaging properties as described above , remains unaffected .but other eigenvalues and eigenvectors change , and modify evolution .an example with two interacting species illustrates the possibilities . in this case , the solution of eq.(1 ) in terms of the ( unnormalised ) right eigenvectors of the evolution matrix is :  are small , .the evolutionary behaviour depends on their signs : + ( a ) : the asymptotic population is proportional to . andthe transient part proportional to fades away .the two species coexist , and their population ratio is stable against small perturbations . such a behaviour does not occur in quantum algorithms .+ ( b ) : both and contain negative components , and so the non - negative population vector has to be a mixture of the two .in course of evolution , the population with is monotonically driven to zero .thereafter evolution has to continue in the reduced dimensional space .+ ( c ) : the eigenvalue , and dominance of drives one of the to zero . the relative size of initial populations ( i.e. comparison of vs. ) determines which is driven to zero .afterwards evolution has to continue in the reduced dimensional space .such a dependence on the initial populations is quite distinct from the `` mini - max analysis '' .these results for two interacting species have a topological interpretation .the three regimes can be looked upon as minimisation of a function over an interval , when it ( a ) has a single minimum , ( b ) is monotonic , and ( c ) has a single maximum .the relation between linear evolution and gradient of a quadratic form is generic , and the features exhibited in the above example can be expected to generalise to more complicated multi - species systems . specifically , whenever some : + ( 1 ) the non - stationary eigenvectors play an important part in evolution .+ ( 2 ) having any makes the stationary eigenvector unstable , and drives the system towards reduced dimensionality .+ ( 3 ) evolution one by one eliminates species with some , till the reduced dimensional system no longer has any .+ ( 4 ) the elimination of species takes place in finite time , which depends on initial populations and , but is roughly .this is in contrast to exponentially decaying tails of transient parts in an altruistic evolution .+ ( 5 ) the surviving population is given not by the stationary eigenvector of the original system , but by the stationary eigenvector of the reduced dimensional system .the simple model presented above provides a quantification of features anticipated in darwinian evolution .the crucial ingredient has been the limited availability of a resource leading to destructive interference .chance mutation may introduce a species that snatches away the resource from another one .this always produces an instability , which eliminates the weaker species in a finite time .the stronger survivors are stable until the next mutation instability .it is worthwhile to observe that the elementary components of biological systems are so simple and cheap that they can be produced in large numbers even with limited resources . as a result ,biological systems often exhibit wastefulness , e.g. millions of eggs and pollen grains are produced when a few would have sufficed to propagate the species in a secure environment .such an overkill actually strengthens the competition and enforces survival of the fittest .  to summarise ,the analysis presented in this article is straightforward , and points out certain similarities between competitive evolution , zero - sum games and quantum computation .the latter two possess a sound mathematical framework , and so even a simple analogy with them can help us understand better the behaviour of highly complex biological systems .the analogies are not perfect , however , and the effect of the differences has to be incorporated properly in the results .my conclusion is that limited availability of resources leads to competition , which eliminates the weaker species in a finite time .the arguments presented here can also be applied to other competitive situations , e.g. economic and social interactions .

Abstract: competition for available resources is natural amongst coexisting species , and the fittest contenders dominate over the rest in evolution . the dynamics of this selection is studied using a simple linear model . it has similarities to features of quantum computation , in particular conservation laws leading to destructive interference . compared to an altruistic scenario , competition introduces instability and eliminates the weaker species in a finite time .