based on the particular properties of single quantum systems , quantum key distribution ( qkd ) promises cryptographic key exchange over an untrusted , authenticated public communication channel with information theoretic security .significant academic , and industrial effort has been devoted to the development of point - to - point ( p2p ) qkd systems based on attenuated laser pulses or entangled photons , and the first fully functional prototype of a quantum cryptographic network consisting of pre - established p2p links in a trusted node scenario has recently been demonstrated ( see also ) .furthermore , various proof - of - principle demonstrations of quantum teleportation and quantum memory ( see and references therein ) have been reported , which will eventually allow building of fully quantum enabled networks , e.g. for perfectly secure communication in settings with un - trusted nodes and over large distances .  despite these remarkable achievements ,the building of a reconfigurable real - world qkd network still requires significant progress , even when limiting quantum communication to qubits encoded into faint laser pulses and to entangled qubits . among the issues to be solvedis the necessity to route quantum data from any sender to any receiver .the possibility to use active optical switches to send quantum information to different users has first been demonstrated in 2003 .however , the question regarding the addition of sender and receiver addresses to the quantum data ( which is not required in pre - established p2p links ) has , to the best of our knowledge , never been addressed . beyond routing ,another requirement for quantum networks is path stabilization between sender and receiver , i.e. to ensure that carriers of qubits prepared at alice s arrive unperturbed at bob s .this includes control of the properties of the quantum channel , e.g. birefringence in an optical fibre , and the establishment of a common reference frame at alice s and bob s , e.g. a direction or a precise time - difference , depending on the property chosen to encode the qubit .current p2p qkd systems are either of the plug & play type and automatically stabilize the quantum channel , or achieve unperturbed quantum communication by adding from time to time short sequences of classical control information . however , neither method allows communication of the properties that are important in reconfigurable networks , including sender and receiver address , or the specific qkd protocol or type of qubit encoding chosen .  in this articlewe propose the use of quantum frames as a flexible framework for sensing , communicating and controlling the parameters relevant in a qkd network setting .our approach is sufficiently flexible to accommodate for current and future quantum technology or applications , including technology from different vendors , which is important in view of open quantum networks .we demonstrate the suitability of our solution for quantum key distribution with polarization qubits over a 12 km real - world fibre optic link .  this article is organized as follows : in section [ sec2 ] we present the general idea of quantum frames .we then discuss the principle qkd setup ( section [ sec3 ] ) , and give further details of key components ( section [ sec4 ] ) . after presenting the properties of our fibre optics link ( section [ sec5 ] ) ,we describe the qkd field tests and discuss the results ( section [ sec6 ] ) , and then elaborate briefly on some issues related to the security of the key establishment ( section [ sec7 ] ) . in section [ sec8 ]we present the status of our classical post processing , required to distill a secret key , specifically the possibility of hardware implementation of one - way error correction .we present our conclusions in section [ sec9 ] .to add control functionalities to the communication between alice and bob , we propose supplementing the quantum data ( e.g. qubits ) with classical control frames . the control frames ( c - frame ) , encoded into strong laser pulses , alternate with the quantum data , and a pair of classical / quantum data forms a quantum frame ( q - frame ) , see .the c - frame allows synchronizing sender alice and receiver bob , facilitates time - tagging , and provides a platform to communicate sender and receiver address ( for routing or packet switching ) plus implementation specific information such as encoding ( e.g. polarization or time - bin qubit ) and protocol ( e.g. bb84 , decoy state , or b92this is interesting in view of open , reconfigurable networks comprising different qkd technologies .the classical information in our implementation is encoded into specific polarization states , allowing assessment and compensation of time - varying birefringence in the quantum channel .note that the compensation scheme can easily be adapted to other qkd setups employing e.g. time - bin qubits , entanglement , or quantum repeaters .furthermore , the c - frames can be used to asses channel loss , which may be important for routing .  ,, width=453 ]  our qkd system is based on polarization qubits , and employs the bb84 protocol  , supplemented with two decoy states  .it allows alternating sequences of strong and faint laser pulses , encoding classical data and quantum data , respectively .a simplified schematic of the qkd system is depicted in .alice uses two laser diodes to generate the classical data ( ld ) and the quantum data ( ld ) .the pulses emitted from ld are first attenuated by an optical attenuator ( att ) , and then sent through an intensity modulator ( i m ) to create signal and decoy states with different mean photon numbers . to create vacuum decoy states ,no electrical pulses are sent to ld .the horizontally polarized faint pulses are then transmitted through a polarization beam splitter ( pbs ) , and combined with the strong , vertically polarized pulses from ld .all pulses are then sent to a polarization modulator ( pm ) , where horizontal ( h ) , vertical ( v ) , right ( r ) , or left ( l ) circular polarization states can be created .quantum and classical data is transmitted to bob through a quantum channel . at bob s end, 10% of the light is directed towards a fast photo detector ( pd ) followed by a logic device ( log ) .the detector and the logic device , which were not implemented in our investigation , will read the information encoded in the classical data and take appropriate action , e.g. for clock synchronization , optical routing , or communication of protocol specific information used by bob for the measurement and subsequent processing of the quantum data .the remaining light is split at a 50/50 beam splitter ( bs ) , and directed to two polarization stabilizers ( ps1 , ps2 ) followed by polarization beam splitters ( pbs1 , pbs2 ) and single photon detectors ( spds ) .ps1 ensures that horizontally polarized classical data , and hence qubits , emitted at alice s arrive unchanged at pbs1 .similarly , ps2 is set up such that right circular polarized classical data and qubits emitted at alice s always impinge horizontally polarized on pbs2 . since the transformation in the quantum channel is described by a unitary matrix ( i.e. orthogonal states remain orthogonal ) , our stabilization scheme ensures that qubits prepared in h and v , or r and l states arrive horizontally and vertically polarized on pbs1 or pbs2 , respectively .hence , the two sets of ps , pbs and two spds both allow compensation of unwanted polarization transformations in the quantum channel , and projection measurements onto h , v , r and l , as required in the bb84 protocol .note that our scheme does not prevent h and v created at alice s from arriving in an arbitrary superposition of h and v at pbs2 ( similar for r and l at pbs1 ) .however , these cases do not cause errors as they are eliminated during key sifting .initially , we used a commercial linbo phase modulator ( pm ) and a mach - zehnder intensity modulator in a one - way configuration to achieve fast polarization and intensity modulation . shows the schematics of the polarization modulator , i.e. a phase modulator with polarization maintaining input fibre ( pmf ) whose slow axis is rotated 45 degrees ( r ) with respect to the optical axis of the modulator waveguide , and standard single mode output fibre ( smf ) .hence , horizontally polarized input light , which propagates parallel to the slow axis of the pmf , is split into two components , where each one propagates along one axis of the waveguide . by applying a control voltage to the phase modulator, a phase shift is introduced between the two components , resulting in a polarization modulation .unfortunately , the phase modulator features significant polarization mode dispersion ( pmd ) for 500 ps long optical pulses resulting in a polarization extinction ratio ( per ) , i.e. the ratio between optical power in two orthogonal polarization states , of only 16 db . moreover , we found both the phase and intensity modulator to be temperature sensitive a change of environmental temperature or heating caused by passing a current through the impedance matching resistance inside the modulators causes a variation of the polarization state , or the intensity level , of the output light .this would have a direct impact on the quantum bit error rate ( qber ) and stability of our qkd system .   to overcome these problems, we designed a basic unit " ( see ) consisting of a phase modulator ( pm ) with 45 degree rotated input pmf and a faraday mirror ( fm ) . as explained below , this allows building stable polarization and intensity modulators by means of a go - and - return configuration ( the light travels twice and in orthogonal polarization states through the phase modulator ) .  to explain how the basic unit works, we calculate the polarization evolution of light using jones calculus :     and denote the jones polarization vectors of the input and output light , respectively , and is the polarization transformation matrix of the basic unit :     , , and denote the polarization transformation matrices of the single mode fibre , the polarization maintaining fibre and the waveguide , respectively , and the arrows on top of the matrices specify the direction of light propagation . denotes the effect of the faraday mirror , and characterizes the rotation between the polarization maintaining fibre and the waveguide . assuming that one can neglect all temperature or mechanical stress mediated changes of the properties of the fibres and the waveguide between two subsequent passages of a pulse of light ( around ten nanoseconds in our setup ) , and that these elements do not feature polarization dependent loss , we have   , \\  } \ ] ]  where stands for the adjoint matrix of , and is the phase shift caused by the birefringence of the polarization maintaining fibre .furthermore , we have   , \\  } \ ] ]  where is the most general unitary matrix describing polarization transformations .the matrices of the waveguide are given by   , ~~  \overleftarrow{m}_{\mathrm{wg } } =  \left [  \begin{array}{cc }   1 &  0 \\   0 & e^{-i(\phi^{\mathrm{out}}_{\mathrm{m } } + \phi^{~}_{\mathrm{e}})}\\  \end{array }  \right],\ ] ]  where and denote the phase shifts during the two subsequent passages of the light through the waveguide , as determined by the modulation voltage applied to the waveguide , and refers to an additional , wavelength and polarization dependent phase shift ( leading to pmd ) .the effect of the faraday mirror is to transform the polarization state of an arbitrary input state of light with components into the orthogonal state :    =  \left [  \begin{array}{c }   j_2^ { * } \\   -j_1^ { * } \\\end{array }  \right]\equiv \textbf{j}_{in}^\perp .\label { eq4_fm}\ ] ]  hence , from equation , we obtain the identity   \cdot   \textbf{j}_{in } \\     & =   \left [    \begin{array}{cc }     d^ { * } & -c^ { * } \\     -b^ { * } & a^ { * }\\    \end{array }    \right ] \cdot fm \cdot   \textbf{j}_{in }  } \ ] ]  and thus  ^{\dagger }   \cdot fm \cdot \left [    \begin{array}{cc }     a & b \\c & d \\\end{array }    \right ] \cdot   \textbf{j}_{in}\\   & = \left [    \begin{array}{cc }     a^ { * } & c^ { * } \\     b^ { * } & d^ { * } \\    \end{array }    \right ]   \cdot \left [    \begin{array}{cc }     d^ { * } & -c^ { * } \\     -b^ { * } & a^ { * } \\\end{array }    \right ] \cdot fm \cdot   \textbf{j}_{in}\\   & = ( a^{*}d^{*}-b^{*}c^ { * } ) \cdot \mathbb{1 } \cdot fm \cdot   \textbf{j}_{in}\\   & = det(m^ { * } ) \cdot   \textbf{j}_{in}^\perp ,  }  \label { eq4_mfmm}\ ] ]  where is an arbitrary two - by - two matrix , which may describe wavelength dependent polarization rotations or polarization dependent loss , and is the two - by - two identity matrix .equation shows that any polarization transformation is compensated by the faraday mirror ; the output polarization state is always orthogonal to the input state , regardless of .  calculating the product of all matrices in equation, we obtain   \cdot fm , \\  } \ ] ]  where , , and .accordingly , for a horizontal input state , we find  \\   & = e^{-i (\phi_\mathrm{smf } + \phi_\mathrm{pmf } + \phi^{~}_\mathrm{e } + \phi^{\mathrm{'}}_\mathrm{m } ) } \cdot \left [    \begin{array}{c }     -i e^{i\phi_\mathrm{pmf } } \sin{\delta\phi_\mathrm{m } } \\\cos{\delta\phi_\mathrm{m } } \\\end{array }    \right ] \\    & = e^{-i ( \phi_\mathrm{smf } + \phi_\mathrm{pmf } + \phi^{~}_\mathrm{e } + \phi^{\mathrm{'}}_\mathrm{m } ) } \cdot \left [    \begin{array}{cc }     e^{i\phi_\mathrm{pmf } } & 0\\     0 & 1    \end{array }    \right ]   \cdot \left [    \begin{array}{c }     -i  \sin{\delta\phi_\mathrm{m } } \\\cos{\delta\phi_\mathrm{m } } \\\end{array }    \right ] .\label{eq4_eout1 } } \ ] ]  hence , owing to the use of a faraday mirror , the polarization and wavelength dependent phase shift introduced by the waveguide impacts now on the global phase but does not lead to polarization mode dispersion any more .furthermore , all ( slow ) modifications of the polarization modulation due to changes in temperature or mechanical stress of the sm and pm fibres are automatically compensated .the output polarization state thus only depends on the modulation of the waveguide ( ) and the phase shift induced by the polarization maintaining fibre ( ) .we complemented the basic unit to a polarization modulator by preceding it by a polarization maintaining circulator ( cir ) that allows separating the input and output optical pulses ( see ) . by applying appropriate , short voltage pulses , which are synchronized with the propagations of the optical pulse , to the phase modulator, we can generate horizontal ( ) , vertical ( ) , right - hand ( ) , or left - hand circular polarization ( ) states .we point out that the existence of the phase introduced by the pm fibre , , makes circular polarization states unstable .however , note that the four generated polarization states always form two mutually unbiased bases , regardless the value of this phase , as required for secure qkd . furthermore , as the change in the polarization maintaining fibre is slow , it can be compensated by a polarization stabilizer at bob s , allowing for the establishment of a sifted key with a small quantum bit error rate ( qber ) .we obtained a polarization extinction ratio of 20 db for horizontal and vertical polarization states ( limited by the light source used to test the polarization modulator ) , see , and of 15 db for left and right circular polarization .we believe the reduced ratio to be caused by state dependent polarization mode dispersion in the circulator , which will be replaced in the near future .  ]similarly , we built an intensity modulator by preceding the basic unit by a pbs , as shown in .the pbs reflects the vertical component of the impinging light .hence , by varying the polarization state of the light at the output of the basic unit , we can vary the intensity of the vertical component at the output of the pbs .  the intensity extinction ratio , i.e. the ratio between the maximum and minimum intensity at the output of the pbs , exceeds 20 db ( see ) .moreover , as the phase , , does not impact on the output intensity , our modulator features an outstanding stability , as depicted in .this is important when implementing a decoy state qkd protocol , which relies on accurate preparation of average photon numbers per faint laser pulse .the link consists of two single - mode dark fibres connecting laboratories at the university of calgary ( u of c ) and the southern alberta institute of technology ( sait ) , see .the fibres , which we refer to as channel 1 and channel 2 , run through tunnels on the two campuses , and are buried or run through train tunnels in between the two institutions .they feature insertion loss of 7.8 db and 6.5 db , respectively .the fibre length is 12.4 km while the straight - line distance between the two laboratories is 3.3 km .a 1300 nm optical time - domain reflectometer ( otdr ) with a 1 km dead zone eliminator was used to characterize the installed fibres .figure [ fig5_2 ] shows the measured otdr traces .the figure clearly shows that the last several kilometers of fibre have bad connections , which result in high transmission loss in our system .the peaks at the distance of 1 km are induced by the core diameter mismatch between the tested fibre and the dead zone eliminator , where the latter one is a multi - mode fibre .we experimentally studied the time evolution of polarization in the installed fibre . in the experiment ,a stable polarized light source was launched into the fibre link , where channel 1 and channel 2 were looped at sait .we used a polarimeter to record stokes parameters of the output light every second .figure [ fig5_3a ] presents the results of one - week of continuous monitoring from april 16 , 2008 to april 24 , 2008 .figure [ fig5_3b ] shows the temperature curve for the calgary airport during the measurement ( data from canada environment weather office ) . comparing figure [ fig5_3a ] and figure [ fig5_3b ] , we observe a clear correlation between the variation of temperature and the fluctuation of polarization .this phenomenon is particularly obvious for the measurement from april 19 to april 23 , where we observe small polarization variation during night , and much more pronounced variations during day - time .figure [ fig5_3c ] is a zoom - in of the measurement on april 19 ( around lunch time ) , where particularly rapid polarization fluctuations are observed . even for this case, we find that the polarization is stable on a time scale of tens of seconds .this sets an upper limit to the duration of quantum data between consecutive stabilization cycles ., width=491 ]  a schematic of the complete experimental setup is shown in .a 10 gs / s function generator ( fg1 ) with two independent outputs drives the quantum laser diode ( ld ) and the classical laser diode ( ld ) via broadband rf amplifiers ( aps ) .both laser diodes produce horizontally polarized optical pulses with a duration of 500 ps and a repetition rate of 50 mhz . by adjusting the temperature, we could closely match the spectral properties of the two laser diodes .we obtained center wavelengths of 1548.07 nm and 1548.11 nm , and spectral widths ( fwhm ) of 0.214 nm and 0.224 nm for ld and ld , respectively .this is important to ensure that the polarization transformation sensed by means of the c - frames ( generated with ld ) equals the one experienced by the quantum data ( generated with ld ) .the pulses from ld , eventually encoding quantum data at different mean photon numbers , propagate through a two - by - two polarizing beam splitter ( pbs ) and enter the intensity modulator , which is described in detail in . to reduce their energy to the single - photon level, a fixed optical attenuator ( att ) is placed between the faraday mirror ( fm ) and the phase modulator ( pm ) .birefringence and polarization dependent loss of the attenuator are automatically compensated by the faraday effect and therefore a stable attenuation is achieved . at the output of the pbs ,the now vertically polarized weak laser pulses are combined with the horizontally polarized strong pulses from ld , which encode the c - frame , to form a complete q - frame .quantum and classical data is then sent through the polarization modulator , which is also presented in .the intensity and the polarization modulator are driven by a function generator ( fg2 ) with a pulse width of 4 ns .note that the polarization maintaining circulator ( cir ) that is part of the polarization modulator only allows horizontally polarized light to enter , while the pulses from ld and ld impinge with orthogonal polarization .therefore , we aligned the axes of the polarization maintaining fibre at the output of the pbs at 45 degrees with respect to the axes of the polarization maintaining fibre at the input of the circulator .this alignment makes the circulator work with both directions of polarization , yet , at the expense of 3 db loss .finally , the polarization modulated data is forwarded to bob through fibre channel 2 .alice s electronic equipment is synchronized using a clock signal at 10 mhz from a clock generator ( cg ) . using a function generator , a laser diode ( ld ) , a photodiode ( pd ) , and a delay generator ( dg ) , the clock signal ( reduced to 1 mhz ) is also transmitted to bob , where it provides trigger signals for the single photon detectors , synchronized with the arrival time of the quantum data .  at bob s side ,90% of the optical power encoded into each q - frame is transmitted through a 10/90 beam splitter and is then equally divided by a 50/50 beam splitter . for each part, the c - frames are sensed by a polarization stabilizer ( ps , from general photonics ) to compensate for the polarization change in the transmission line , and the quantum data is detected by a measurement module consisting of a pbs and two ingaas based single photon detectors ( spds ) .the spds are triggered at 1 mhz , and operated with a gate width of 5 ns , a deadtime of 10 and a quantum efficiency of 10% .  in principle , the length of a c - frame is determined by the response time of the polarization stabilizer , which is 18 ms .however , due to the small duty cycle of the classical pulse sequence in the current implementation and the low transmission of the fibre link , the average power of the c - frame is below the detection threshold of the polarization stabilizer . to resolve this problem, we placed a polarization maintaining erbium doped fibre amplifier ( edfa ) between ld and the pbs .the edfa is turned off after each c - frame to avoid flooding the spds at bob s with photons from amplified spontaneous emission . while the turn - off time is only tens of milliseconds ( consistent with the radiative lifetime of population in the upper laser level ) , we found the turn - on time of the edfa to be as long as 3 seconds , resulting in 5-second long c - frames .the length of quantum data is set to 2 seconds , according to the worst - case " polarization stability of the fibre link , which is discussed in . from this , we find that our setup currently limits the time for quantum key distribution to 30% of the operation time . note , however , that the duty cycle of the classical pulse sequence can easily be increased by several orders of magnitude . in this case the duration of a c - frame would be limited by the response time of the polarization stabilizer , and the time for qkd could exceed 99% of the system s operation time .we performed a variety of measurements to assess the performance of our qkd system . for _2-detector measurements _ , alice repetitively creates sequences of q - frames with polarizations hh , hl , hv , hr , lh , ll , lv , lr , vh , vl , vv , vr , rh , rl , rv , and rr .the first letter indicates the polarization of the c - frame and the second one indicates that of the quantum data .bob uses one measurement module to process the frames .the polarization stabilizer compensates the polarization transformation in the quantum channel for states belonging to the basis indicated by the first letter , i.e. linear or circular . for _4-detector measurements _ , alice modulates the polarization of the q - frames in the more complicated order of hh , rh , vh , lh , rh , hh , lh , vh , hr , rr , vr , lr , rr , hr , lr , vr , hv , rv , vv , lv , rv , hv , lv , vv , hl , rl , vl , ll , rl , hl , ll , vl .bob uses two measurement modules to process the q - frames .the polarization stabilizer of one module is always activated for odd frame numbers , and that of the other module is always activated for even frame numbers ( see ) . in this way, the two measurement modules compensate polarization transformation for states encoded in the linear , or the circular basis , respectively .we collect the number of trigger events and counts for all single photon detectors for each combination of polarization states and different mean number of photons per qubit .this allows calculating average quantum bit error rates ( qber ) and key generation probabilities ( kgp ) , where the kgp is defined as the probability of generating a sifted key bit from a qubit encoded into a weak signal state when alice and bob use the same basis :    the probabilities for correct ( ) and wrong sifted key bits ( ) are obtained from experimental data by dividing the number of correct , or wrong , detection events by the number of trigger events .we assume that the probability for both detectors to click simultaneously can be ignored . in our setup , it was at least four orders of magnitude smaller compared to the probability for a single click .note that in an actual implementation simultaneous clicks in two or more detectors have to be replaced by a randomly selected detection event .assuming that the photon number per laser pulse satisfies a poissonian distribution , and can be calculated using     is the probability for a detector click without alice sending a photon , which includes detection events due to dark counts and stray photons .we found this probability in our setup to be equivalent to the dark count rate . is the average photon number of the weak pulses at alice s output , is the overall transmission , which includes the fibre link and bob s optical components , and is the quantum efficiency of the single photon detectors .finally , describes the polarization extinction ratio of the pbs , i.e. the probability for a horizontally polarized photon to be transmitted through the pbs , normalized to the probability to exit .the experimental results of the measurements are summarized in , together with the theoretical predictions .note that all parameters required to calculate the qber and the kgp have been obtained through independent measurements .we see that the experimental values match the theoretical calculations very well .we also find that the average qber of the 4-detector measurement is larger than that of the 2-detector measurement at the same mean photon number .this is due to an increased dark count probability of the two additional spds , and slightly worse alignment of the polarization stabilizer in the second measurement module .furthermore , the 4-detector measurement features a higher kgp as no qubits are lost at the 50/50 beam splitter .the individual data of the 4-detector measurement with an average photon number of 0.5 photons per pulse is listed in .c|rrc|rrc  & & + & & & & & & + hh & 1,569 & 13,254,716 & .27 & 37,639 & 12,504,218 & .21 + hv & 39,642 & 13,381,789 & .28 & 1,922 & 13,385,381 & .43 + rr & 1,243 & 13,160,359 & .25 & 35,711 & 12,443,131 & .42 + rl & 41,856 & 13,521,618 & .09 & 1,979 & 13,505,244 & .34 + vh & 42,567 & 12,853,157 & .80 & 950 & 12,863,193 & .32 + vv & 1,569 & 13,183,509 & .24 & 34,723 & 12,454,406 & .55 + ll & 41,800 & 13,514,989 & .10 & 1,841 & 13,114,840 & .53 + lr & 959 & 10,908,918 & .56 & 30,270 & 10,273,810 & .31 +  & & + & & & & & & + hh & 37,577 & 12,468,543 & & 1,050 & 12,416,198 & .73 + hv & 2,121 & 12,145,604 & .58 & 35,843 & 11,410,147 & .03 + rr & 35,954 & 12,409,015 & .38 & 1,605 & 12,351,662 & .86 + rl & 3,222 & 12,253,689 & .80 & 36,378 & 11,541,004 & .01 + vh & 2,410 & 12,817,201 & .26 & 39,290 & 12,046,285 & .86 + vv & 36,215 & 12,403,829 & .35 & 925 & 12,355,805 & .26 + ll & 2,751 & 12,270,811 & .49 & 36,547 & 11,534,262 & .99 + lr & 29,988 & 10,247,919 & .34 & 1,149 & 10,193,024 & .48 +   to study the stability of the system , we performed a long time measurement over 37 hours .in the measurement , alice sends qubits encoded into weak laser pulses with an average photon number of 0.5 , and bob implements a 2-detector measurement using measurement module one . at the end of each c - frame ,i.e. after stabilization , bob records the polarization of the c - frame with ps1 .meanwhile , the polarization stabilizer ( ps2 ) in the second measurement module monitors the polarization of the c - frame without polarization control . in, the red points indicate the stokes vectors of the classical pulses measured by ps2 , which are randomly distributed on the surface of the poincar sphere due to the time - varying polarization transformation in the transmission line .the blue points depict the measurements made by ps1 , i.e. after polarization control .even though the result slightly deviates from a single spot , which is expected in the ideal case , it clearly demonstrates the good long - term stability of our qkd system .  for a more quantitative analysis, we also recorded the evolution of the qber over the same time interval , see .the temperature curve for the calgary airport ( data from canada environment weather office ) is shown as well .the qber varies between 2.85% and 3.35% in over 35 hours , and the variation is less than 0.1% in the last 15 hours .for any cryptographic system , be it of quantum or classical nature , it is important to carefully analyze the actual implementation for weak points that may compromise its principle security . applied to quantum key distribution , these include deficiencies in the preparation of quantum data at alice s that can be exploited by an eavesdropper to gain information about the sifted key .we refer to these kind of attacks as _ quantum state attacks_. furthermore , eve may also attempt to actively sense the classical devices that create or measure the quantum data , or try to actively impact on the interaction between quantum and classical systems to influence the outcomes of measurements .we refer to these kind of attacks as _ classical system attacks_.  note that , once the deficiencies are found , it may be possible to eliminate them by devising a better optical setup , or to remove the corresponding amount of information that eve may have obtained through additional privacy amplification . yet, we point out that loopholes may also arise from a careless implementation of privacy amplification , e.g. improper choice of hash function , or of insufficient authentication of the classical channel . finally , the size of the error corrected key has to be considered when calculating the appropriate amount of privacy amplification , i.e. to distil a secure key .  in the following, we will briefly discuss our current optical setup in view of such weak points .yet , a complete security analysis of our system is beyond the scope of this article , which is the introduction of quantum frames .note that the existence of loopholes in a particular qkd setup breaks the unconditional security of this particular system , but does not disprove that qkd can , in principle , be information theoretic secure .the use of attenuated laser pulses , as opposed to pairs of entangled photons , entails the possibility that non - orthogonal qubit states ( here encoded into the polarization degrees of freedom ) may become distinguishable when taking into account other degrees of freedom needed to fully describe the quantum data , e.g. frequency , temporal modes , or transverse modes .obviously , in this case , the security offered by qkd would break down .we refer to these attacks as _ quantum side channel attacks_. furthermore , as the number of photons in the attenuated laser pulses is described by a poissonian distribution , it may be possible for an eavesdropper to gain information based on _ photon - number - splitting ( pns ) attacks_.   in our qkd system , all four qubit states are produced by the same laser diode , which is triggered independently of the subsequent action of the polarization or intensity modulators . together with the polarization independent spectral transmission of both modulators and the attenuator , due to the use of the faraday mirrors, this ensures that correlation between polarization state and spectrum or temporal mode do not exist .however , we recall that the circulator ( cir ) at the output of the polarization modulator adds basis dependent polarization mode dispersion , which manifests as a basis dependent qber. this may induce detectable temporal broadening of the photonic wavepackets , i.e. may partially reveal the basis used for encoding the qubit .the circulator will be replaced in a future , improved setup .furthermore , as the entire setup is built with ( transverse ) single mode optical fibres , correlation between polarization states and transverse modes , which may be present in a free space system , are ruled out .the use of faint laser pulses makes our system principally susceptible to photon - number - splitting ( pns ) attacks , which were first mentioned in and have been analyzed thoroughly in . a possibility to remove the threat of the pns attack is the use of so - called decoy states allows establishing a conservative lower bound for the key that can be created from single photons emitted at alice s , i.e. key that was not subject to the pns attack .as described before , our setup has been devised to allow for the implementation of decoy states . in the followingwe will examine experimentally the accuracy with which the decoy state method allows bounding the size of the secret key .  with the gllp method the secure key rate per emitted faint pulse with meanphoton number of is given by     \label{eq7_1}\ ] ]  where the factor accounts for basis reconciliation , denotes the shannon entropy , , , and specify the gains and error rates of signal states and single photons , respectively , and is the error correction efficiency which is assumed to be 1.22 .  in the first analysis , we assume that no pns attack took place during the measurement , which is a reasonable assumption . using equations , we can estimate the gain and error rate for signal states with mean photon number :    similarly , the gain and error rate for single photon pulses are given by    using equation , and and taking into account the measured values for , , and , we can calculate the secret key rate for different , see curve a of .  in the second analysis , which again relies on the assumption of fair loss, we use equation to calculate the gains and error rates for the signal state with mean photon number and the decoy state with mean photon number of 0.1 . to calculate the gain and error rate for single photon pulses , we use equations ( 34 ) , ( 35 ) and ( 37 ) from :    the resulting secret key rate follows from equation .it is shown in curve b of .finally , we calculate the secret key rate using the experimentally measured gain and error rates for signal and decoy states , as opposed to the previous case where they were calculated . the gain and error rate for single photons are estimated as before using equations ( [ eq7_6 ] ) .the result is plotted in curve c of .note that the measurement does not rely on the fair loss assumption .  ]  comparing the three different curves , we find that the rates estimated from the decoy state method ( curves b and c ) is somewhat smaller than the one plotted in curve a. this is natural as the decoy state method with decoy states of finite photon mean number only yields a conservative lower bound . as an example , for , we find the secret key rate ( curve b and c ) to be roughly 10% worse than the secret key rate given in curve a. we also find a reasonably good agreement between the rates estimated and measured using the decoy state method ( curves b and c , respectively ) .we attribute the remaining discrepancy to a systematic error in the estimation of the single photon gain , resulting from a slightly wrong estimation of the transmission in the link , quantum efficiency of the detectors , or error rate due to wrongly received photons .factors like fluctuations in the mean photon number could also have an effect .this systematic error also affects the estimation of the single photon error rate .furthermore , curve b and c show that the secret key rate in our qkd system is maximized for signal states with a mean number of photons of .this value agrees with estimations in when taking into account the actual values for dark count rates , transmission , detector quantum efficiency , and error rate caused by wrongly received photons .indeed , we calculate , in very good agreement with our experimental results .to finish this discussion , we emphasize that the secret key rate in an actual implementation of an information - theoretic secure qkd session must be calculated using the decoy state method used in the third analysis and must not rely on assumptions about fair loss in the quantum channel .we have noted that each faint pulse that encodes a qubit is preceded by another faint pulse , originating from a reflection on the pbs that is part of the intensity modulator ( see section [ sec4 ] ) .note that the number of photons in both pulses is comparable .obviously , for our assessment of the eavesdropper s information to be correct , we have to make sure that this pulse , which also transits through the polarization modulator , does not encode any polarization information .therefore , we have carefully adjusted the electrical trigger signal for the polarization modulator such that it only acts on the real " faint pulse , and not on the spurious one .    as in any qkd system , regardless whether it employs one - way or two - way quantum communication , appropriate measures have to be implemented to protect against trojan - horse attacks . in these attacks ,the eavesdropper injects light through the optical fibre into alice s or bob s preparation or measurement device , respectively , and analyzes the back reflection , which may reveal information about the quantum state created at alice s or the measurement basis to be used at bob s . in both cases ,the security of the key distribution would be compromised as eve either knows the state , or knows in which basis to perform an intercept resend attack without creating errors . in our qkd system ,given the static setup at bob s , trojan horse attacks have to be considered only at alice s . towards this end, a polarization independent optical isolator and a spectral filter that absorbs all wavelengths not blocked by the isolator should be placed at the output of alice s .   in a time - shift attack eavesdropper exploits the fact that the detection efficiency of different detectors may , for a given arrival time of a photon , be different .it may thus be possible for an eavesdropper to bias the detection probabilities by actively time - shifting the arrival time of photons and thereby acquire information for each photon if it was detected in a detector that codes for a bit value 0 , or 1 .this attack , which is possible in our current system , can be overcome if bob randomly rotates the polarization state of each incoming qubit by 0 or , thereby de - correlating a detection in a particular detector with a particular bit value .this can be done by placing a rapidly variable waveplate in between the polarization stabilizer and the pbss , at the expense of rendering bob s setup active " , i.e. vulnerable to trojan horse attacks ( which then have to be protected against , as discussed above ) .once the quantum part of the qkd protocol is finished , alice and bob must perform a series of classical steps to go from the raw key to the secret key used for encryption .the steps required are shown in .in addition to sifting , error correction is used to ensure that alice and bob have an identical key despite any errors that occur .privacy amplification is then used to eliminate any information eve has obtained about the key , whether through eavesdropping on the quantum channel or on the classical communication used for error correction . these steps must also make use of authenticated communication to prevent eve from performing a man - in - the - middle attack . of these steps, error correction is expected to become the bottleneck in the qkd system once higher raw key rates are achieved .the cascade protocol  that was originally developed for qkd is not suitable for high key rates as it requires many rounds of communication between alice and bob and is computationally expensive  .  ]low - density parity - check ( ldpc ) codes were originally developed by gallager in the 1960s  for classical communications , but their potential performance has only been recently been discovered  .ldpc codes for qkd differ slightly from those used in the classical case as the parity information is transmitted over a separate classical channel  .a ldpc code is defined using an parity check matrix , , consisting of zeros and ones .while either alice s or bob s sifted key may be considered the correct " key for the purpose of error correction , this discussion will use alice s sifted key , the bit column vector , i.e. one - way , forward error correction .alice computes a parity vector as follows :    where the number of bits in the parity vector is lower bounded by shannon s noisy coding theorem ; with shannon entropy .thus , indicates whether the sifted key bits indicated by the ones in the row of contain an even ( =0 ) or odd ( =1 ) number of ones .alice transmits to bob , whose task it is to determine using , , his sifted key , , and an initial estimate of the qber .this estimate can be based on a characterization of the quantum channel or on the qber from previous executions of the protocol .  in order to recover , bob uses a process known as belief propagation to refine his initial probabilities for the entries of based on and the qber . note that in the following discussion , bob has full knowledge of his key vector , , but his knowledge of the alice s key vector , is probabilistic .for example , suppose row of is a parity check on three bits received by bob , , , and , where the expected qber is 10% ( chosen to prevent very small numbers in this example ) .the probability that a key bit is zero or one based on the received values and the qber are denoted and , respectively . for each of his bits , bob assumes that and computes , which denotes the probability that the parity check is satisfied ( ) given this assumption .alternatively , may be viewed as the probability that given the value of and what is known about the other bits of involved in the parity check .for example , may be computed as follows :    as can be seen in , the probability that the bits retain their received value is high when since this is consistent with the received values of . if instead , a high probability for bit flips is obtained since each row assumes that the received values for the other bits are likely to be correct .this information is useful when combined with the results of other parity checks . & & & & for & for + 1 & 1 & 0.1 & 0.9 & & + 2 & 1 & 0.1 & 0.9 & & + 3 & 0 & 0.9 & 0.1 & & +  after doing these computations for each row of , bob uses the information from all the parity checks involving a particular key bit to compute new values of and .if the key bit is involved in three parity checks , bob computes and , which represent the probability that is zero or one , respectively , based on and the qber , and that all parity checks involving are satisfied :   where .since valid results must be consistent with all parity checks , and are obtained by normalizing and .for example , consider , implying and as shown in .even if one parity check suggests there is an error in this example , the confidence that ( i.e. was received correctly ) still increases . with all three parity checks suggesting a bit flip is necessary , a high confidence is obtained that the received value of is incorrect . with two parity checks suggesting a bit flip is required , the result does not significantly favour either result .bob can then select the most likely value for each bit to form , and compute . if , the protocol is finished. otherwise , additional iterations of the protocol are performed . with the additional modificationthat bob also computes conditional probabilities , and , to use in during subsequent iterations , this procedure is generalized as the sum - product algorithm  . & & & & & & + 0.82 & 0.82 & 0.82 & 0.0006 & 0.4963 & 0.0012 & 0.9988 + 0.18 & 0.82 & 0.82 & 0.0027 & 0.1089 & 0.0238 & 0.9762 + 0.18 & 0.18 & 0.82 & 0.0121 & 0.0239 & 0.3361 & 0.6639 + 0.18 & 0.18 & 0.18 & 0.0551 & 0.0052 & 0.9131 & 0.0869 +   interest in ldpc codes stems not only from their potential to perform near the shannon limit .since the computations for each parity check and each key bit are independent , the structure of the sum - product algorithm lends itself to parallel computation .this makes sum - product decoding of ldpc codes well suited for high speed implementation in custom hardware or in reconfigurable devices such as field programmable gate arrays ( fpga )  .however , floating - point computations are expensive in terms of the amount of logic required .thus , it is desirable to implement ldpc decoding using fixed - point arithmetic ( equivalent to integer arithmetic ) with as few bits as possible to represent the values . in initial simulations of fixed - point decoding, we found that the primary obstacle for a small bit length was the very small values obtained for the probabilities .this problem manifested as divide by zero " errors during the normalization since both and had rounded to zero .we overcome this limitation by modifying the algorithm to set any occurrences of zero in the values to the smallest possible non - zero value .a ldpc code was designed with a parity check matrix using parameters similar to  ( qber=3% , parity checks on 20 key bits .note that this qber also reflects our experimental results , see section [ sec5 ] ) .it has been shown that having the key bits take part in a variable number of parity checks results in better performance  .thus , has a fixed number of ones in each row , known as the row weight , and a variable number of ones in each column , known as the column weight .the method presented in  was used to determine the column weights by applying a well known optimization technique with the constraints ensuring that the design criteria ( qber and code rate ) are met . in place of the arbitrary cost function in  , we use a function reflecting the computational complexity .our code was simulated over 40 iterations , with the number being selected based on tests which showed very little improvement beyond this point . the results in show that 24-bit fixed - point and floating - point have very similar decoding performance .ldpc code using 16-bit fixed - point ( , ) , 24-bit fixed - point ( , * ) , and floating - point ( , ) .the inset shows the region where the performance begins to drop in more detail.[fig8_2 ] ]  using vhdl ( a hardware description language ) code generated in matlab , we are able to create code for parallel implementations of sum - product decoding for arbitrary values of . while a rtl ( register transfer level ) simulation of the ldpc code is possible , a fully parallel implementation is not possible at this time .a ldpc code with a row weight of 12 that is capable of operating at 50mhz was synthesized using the artisan 3.0 logic cell library for 0.18 cmos technology ( several generations behind state of the art ) .this code uses 12-bit arithmetic and requires 46 clock cycles ( 0.92 ) per iteration of the algorithm .simulation results for the performance of this code with a maximum of 40 iterations are given in .the design contains 1860429 cells with a total cell area of approximately 47.24 .attempts to synthesize a larger ldpc code using the current vhdl code have failed as the synthesis tool does not have sufficient memory to complete the process .the size of the design also suggests that a code would be impractical to implement ( as a comparison , a processor is typically on the order of 100 , including interconnect ) . however , larger codes are preferred because they experience less variance from the mean qber and perform better relative to the shannon limit . qber ( % ) & success rate ( % ) & mean iterations & sifted key rate ( mb / s ) + 2.5 & 99.00 & 4.1070 & 52.9319 + 3.0 & 91.65 & 8.6785 & 25.0494 + 3.5 & 69.80 & 17.9455 & 12.1146 +  it is important to note that we obtained these results without using any advanced techniques to reduce the size of the design .more efficient multiplier designs or the use of alternative number systems such as the multidimensional logarithmic number system ( mdlns )  have the potential reduce the hardware required to perform the computations .larger block sizes could also be achieved using the partially parallel implementations proposed in  , where efficient schedules are used rather than updating all probabilities at once , reducing the number of computations done in parallel while mitigating the cost in terms of the run time .we have proposed a novel , fibre - based qkd system employing polarization encoding and quantum frames , and have demonstrated in a long - term ( 37 hours ) qkd proof - of - principle study that polarization information encoded in the classical control frames can indeed be used to stabilize unwanted qubit transformation in the quantum channel . all optical elements in our setup can be operated at gbps rates , which is a first requirement for a future system delivering secret keys at mbps . in order to remove another bottleneck towards a high rate system , we are investigating forward error correction based on low - density parity - check codes  .work on the implementation of a system that distributes a quantum key , building on the here presented proof - of - concept demonstration , is under way .the authors gratefully acknowledge discussions with xiongfeng ma . this work is supported by general dynamics canada , alberta s informatics circle of research excellence ( icore ) , the national science and engineering research council of canada ( nserc ) , quantumworks , canada foundation for innovation ( cfi ) , alberta advanced education and technology ( aet ) , cmc microsystems , and the mexican consejo nacional de ciencia y tecnologa ( conacyt ) .99  bennett c h and brassard g 1984 _ proc .comput . syst .signal process ( bangalore india ) _ 1759 shor p w and preskill j 2000 _ physlett _ * 85 * 4414 gisin n , ribordy g , tittel w , and zbinden h 2002 _ rev .phys _ * 74 * , 14595 scarani v , bechmann - pasquinucci h , cerf n j , dusek m , lutkenhaus n and peev m 2008 _ preprint _ arxiv : quant - ph/0802.4155 see www.idquantique.com , www.magiqtech.com , and www.smartquantum.com see http://www.secoqc.net   tittel w , afzelius m , cone r l , chanelire t , krll s , moiseev s a and sellars m 2009 _ laser & photonics review _doi 10.1002/lpor.200810056 hammerer k , sorensen a s , and polzik e s 2008 _ preprint _gisin n and thew r 2007 _ nature 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Abstract: we propose a fibre - based quantum key distribution system , which employs polarization qubits encoded into faint laser pulses . as a novel feature , it allows sending of classical framing information via sequences of strong laser pulses that precede the quantum data . this allows synchronization , sender and receiver identification , and compensation of time - varying birefringence in the communication channel . in addition , this method also provides a platform to communicate implementation specific information such as encoding and protocol in view of future optical quantum networks . we demonstrate in a long - term ( 37 hour ) proof - of - principle study that polarization information encoded in the classical control frames can indeed be used to stabilize unwanted qubit transformation in the quantum channel . all optical elements in our setup can be operated at gbps rates , which is a first requirement for a future system delivering secret keys at mbps . in order to remove another bottleneck towards a high rate system , we investigate forward error correction based on low - density parity - check codes .


numerical simulation procedures for designing waveguide couplers to accelerator structures are described in [ 1 ] and an example of its application to the design of the input coupler for the nlc linac is given in [ 2 ] .a coupler cavity is designed with the intent of providing a matched connection between a waveguide and a uniform accelerator structure with dimensions corresponding to those of the cell adjacent to the coupler cavity .a symmetric structure consisting of two coupler cavities ( with associated waveguides ) connected by a short section of accelerator structure ( typically two cells worth ) is modeled and subjected to a ( let us assume single frequency ) time domain simulation .the entire assembly is treated as a single structure with two wave guide ports .the coupler cell dimensions are adjusted until an apparent match is achieved , that is , until no reflection is experienced at the ports ( the external matching condition ) . to eliminate the possibility that the match arises from a fortuitous cancellation between forward and backward waves within the accelerator structure , both the amplitude and phase of the accelerating field on the beam axis are observed and required to have the periodicity and phase advance properties appropriate to a pure traveling wave ( the internal matching condition ) . as a check one may add a cell to the accelerator structure and see whether all these conditions are still satisfied .it is often the case that accelerator structures are slowly varying rather than uniform , in which case the input and output couplers are matched separately .  in practice the procedure ( we refer to it as the standard procedure ) has been quite time consuming , involving trial and error rather than a systematic procedure to simultaneously satisfy both the internal and external matching conditions .another limitation arises from the fact that the method assumes that evanescent bands can be neglected but provides no procedure for demonstrating their absence .  in the next sectionwe describe a new simulation procedure which has been found to be much more efficient , and also which provides information about the presence of evanescent bands .the basic elements of the method were briefly described in [ 3 ] in connection with the design of a coupler for the zipper structure .because it has since replaced the old method for all of our coupler design work , a more complete presentation together with examples will be presented in the following sections .as in the case of the old standard procedure one applies a single frequency time domain simulation by driving the input port of a two port structure consisting of an input cavity , an cell periodic structure with period , and an output cavity .instead , however , of focusing attention on the s parameters of the structure as a whole , we direct our attention to the simulated accelerating field evaluated along the beam axis .we assume a steady state has been reached , so that the subsequent time dependence can be expressed in terms of the complex ( henceforth ) , obtained in the standard way by combining the simulated real fields at two times separated by a quarter period . then from floquet s theorem ( neglecting evanescent bands , losses , and an irrelevant overall phase factor )  .\ ] ]  here is a real positive amplitude function with period , and is a real phase function , periodic except for a cell to cell phase advance .thus     is a independent complex reflection coefficient .note that one is free to shift by an arbitrary constant with a compensating phase shift in , since the overall phase of is irrelevant .this freedom corresponds to the choice of reference plane through some point where we take .we now consider the quantities   where   elementary algebraic manipulation leads to the relations :    /[2sin(\psi)+j\delta(z)].\ ] ]  we note that while the rhs of ( 5 ) is formed of dependent complex quantities , it nevertheless turns out to be real and independent .similarly the absolute value of the rhs of ( 6 ) is also independent .both these results should hold for all `` allowed '' values , i.e. , values such that the three points , , and all lie within the periodic portion of the structure simulated , and together they constitute a powerful constraint on the validity of the floquet representation eq .their failure beyond small numerical fluctuations or small deviation from steady state is evidence for the presence of evanescent bands .an example will be presented in the section on the zipper structure .it is noteworthy that these relations allow one to determine all the properties of the traveling wave solutions , including the functions and from a simulation which contains an arbitrary mixture of forward and backward waves .of particular importance is the fact that it gives the magnitude and phase of the reflection coefficient .in contrast to the old standard method , there is here only one matching condition to be satisfied , namely .typically match is achieved by varying two parameters in the coupler design .once one has determined how the real and imaginary parts of vary with the parameters , one can choose linear combinations of changes which accelerate the process of converging to the origin in the complex plane [ 4 ] . because the phase of does depend upon the position of the reference point relative to the couplers , one naturally keeps it fixed while carrying out this process .note that it is the output cavity that is matched by this procedure . while not necessary , it is usually convenient to construct a symmetric mesh .the input and output cavities are then the same , and the structure as a whole is matched when vanishes ._ ( a ) the nlc four port output coupler _  as an example of the principal features of the new method we use the new nlc four port output coupler cavity [ 5 ] .the purpose of the four port design was to provide damping for those dipole modes that reach the end of the structure while also providing an output for the accelerating mode .these dipole modes are typically those which had been poorly damped because of decoupling of the last cells from the manifolds .the four port symmetry provides damping for both dipole mode polarizations and has the added advantage of eliminating quadrupole distortion of the coupler fields .the design simulation was carried out with a three cell periodic structure , and results are illustrated in fig .two cases are shown , one matched , the other not .the reflection coefficients as computed from eq .( 5 ) for the two cases are shown as functions of .the allowed z values are those lying within the central cell , and one sees that for both cases is constant over that range . the real part of is also plotted as a function of .one sees that the two values are indeed constant over the allowed range , but contrary to expectations they differ somewhat from each other and from the expected value of one half .this is due to the fact that a different and coarser mesh than that used to determine the phase advance parameter was used for the time domain simulations .the two cases differ from one another because the parameter variations in the coupler associated with the matching procedure induce small but global changes in the meshing .it has been confirmed in a number of cases that there is good agreement between the phase frequency relation determined from single cell periodic boundary condition frequency domain calculations and that determined from the time domain method described here so long as the same mesh is used for both simulations .( 100,200)(-10,15 ) = 7.5 cm  _ ( b ) a photonic band gap ( pbg ) structure _  ( 100,200)(-5,-65 ) = 8.5 cm  a coupler cell very similar to those of the slac structures has been designed for a pbg structure , that is , a cylindrical cell with a pair of symmetrically placed waveguide ports , a conventional beam pipe , and conventional beam iris coupling to the periodic pbg structure .the pbg cell structure [ 6 ] is a seven by seven square array of metallic posts aligned in the beam direction and terminated by metallic end plates , the cell cavity being formed by removing the central post .a circular aperture in the end plates , identical to that between the coupler cell and the adjacent pbg cell , provides cell to cell coupling and a path for the beam . a perspective representation of the four cell quarter structure used for the simulations is shown in fig .( 2 ) . also shown is the simulated electric field distribution , scaled logarithmically to enhance the visibility of weak field strengths .the figure illustrates the effectiveness of the pbg structure in confining the acceleration fields to the interior of the structure .the matching procedure worked well , and , as in the four port coupler above , there was no evidence for evanescent band contamination .fabrication of an experimental model with 5 coupled pbg cells and complete with couplers is in progress at slac .  _( c ) the zipper structure _the zipper is a planar accelerator structure described in [ 3 ] .a 25 ( counting the coupler cavities ) cell w band model has been built , cold tested , and subjected to bead pull measurements as reported in [ 7 ] .the design was governed by a decision to avoid bonded joints involving tiny structure elements such as the vanes which serve as cell boundaries and also form the beam iris .the coupler cell is a quarter wave transformer terminating in wr10 waveguide .early attempts at matching the coupler using the old standard method failed , and it was this failure which led to the development reported here . matching using this method was accomplished by making use of a time domain simulation of a structure with 22 periodic cells .3 shows the resultant , , and plots as computed from eqs .( 5 ) and ( 6 ) .one sees large deviations from the expected independent behavior as one moves away from the center of the structure .this effect indicates a clear violation of eq .( 1 ) . from the fact that the violation fades away as one moves away from the couplersindicates that the effect is due to the couplers generating an evanescent band , the nearby monopole band pointed out in [ 3 ] .this example demonstrates how the method indicates the presence of evanescent band interference , and also how one can carry out the matching procedure even when it is present .( 100,200)(-5,-62.5 ) = 8.cmelectrical discharge damage has been commonly observed in the coupler cells of accelerator structures and has been attributed to the field enhancement noted in simulations .we have taken advantage of our enhanced matching capability to initiate a study of this long standing problem .exploration of the situation for the nlc coupler [ 2 ] showed that the largest enhancement occurred on the coupler side of the aperture of the iris separating the coupler from the adjacent cell with azimuthal maxima opposite the coupler waveguides and azimuthal minima 90 degrees away .this observation was consistent with the pattern of discharge damage [ 9 ] .it is pointed out in [ 8 ] that the azimuthal variation is due to the quadrupole component introduced by the coupler waveguides and that the enhancement can be reduced by introducing a racetrack like modification of the coupler cell shape designed to eliminate it .this effect and its cure have been confirmed in our own studies of the nlc coupler .two other modifications have also been explored .the simplest and most effective was simply to reduce the radius of the cell adjacent to the coupler .the effect for a 2 reduction is illustrated in fig .4 where it is seen that the field on the coupler cell iris is significantly less than that on the interior coupling irises .an undesirable consequence is a 10 degree phase advance deficiency in the modified cell .an even larger field reduction would be obtained by removing the quadrupole enhancement .we attribute the reduction to an increase in group velocity . the other modification consisted of enlarging the coupler iris combined with an increase in the adjacent cell radius chosen so as to preserve the cell phase advance , butthe exploration of this effect is incomplete .experimental investigation to determine whether such changes actually do reduce electrical discharge damage in the coupler is clearly needed .

Abstract: we present numerical procedures for analyzing the properties of periodic structures and associated couplers based upon time domain simulation . simple post processing procedures are given for determining brillouin diagrams and complex field distributions of the traveling wave solutions , and the reflection coefficient of the traveling waves by the input and output . the availability of the reflection coefficient information facilitates a systematic and efficient procedure for matching the input and output . the method has been extensively applied to coupler design for a wide variety of structures and to a study directed towards elimination of the surface field enhancement commonly experienced in coupler cells .   0.25 truein  epsf = 100=10000=10000=10000


-wing unmanned aerial vehicles ( uavs ) are essential components of remote monitoring applications like surveillance , mapping , aerial photography , etc . , where the uavs need to cover large regions .typical uavs used for these applications are of low cost with limited fuel capacity and hence require periodic refueling to accomplish the mission .for the case of using low cost uavs , these ones have however limited fuel capacity and require periodic refueling to accomplish the mission. in these scenarios , airborne docking for mid - air refueling has become recently a major research area , see e.g. , .however , the wake effects of the tanker on the uav makes the analysis and design of the control scheme particularly challenging ( e.g. , a large amount of experimental data are needed ) . in ,a passive towed cable system is used to retrieve the uav , thus avoiding wake phenomena . on the other hand ,a robust vision tracking method is required for the uav to overcome some hardware limitations of the vision system ( mostly when the uav gets closer to the drogue ) .the most simple solution is to deploy an immobile base station in a fixed location to oversee the operation and to refuel the uavs , as shown in figure [ fig : scenario1 ] .the base station may be located at a distant which diminishes the utility of the uavs fuel per mission . instead of an immobile unit , an unmanned ground vehicle ( ugv )can be deployed that can refuel the uavs at different locations , and hence reducing the uav refueling time , which increases the coverage area per refuel as shown in figure [ fig : scenario2 ] . in order to accomplish this capability ,there is a need to develop techniques for uav rendezvous with the moving ugv .cooperative uav and ugv teams have been previously used for several surveillance applications .for instance , the uav can provide useful information ( e.g. , data from aerial images ) to the ugv for path planning and target detection . in a different application , tokekar et al . used an uav to acquire points of nitrogen sampling in a field and the ugv used these points to create a path of one - in - a - set . in this paper , we are concerned about using the ugv as a refueling mobile station and hence the uav needs to generate a trajectory such that it can rendezvous with the moving ugv .the uav , ugv rendezvous can be considered either as a docking or landing problem .aerial rendezvous between multiple aircrafts for refueling and formation flight are related but the type of vehicles taken into account are the same and secondly , the rendezvous typically is in 2d , unlike the landing , which is in 3d .carnes et al . developed an auto - takeoff and auto - landing capabilities for a low - cost uav , which is essential for many of the envisioned applications .nonetheless , the trajectories are not optimized , which is one of the key contributions of this paper .kim et al . developed a vision based net - landing controller for a uav .the controller is based on pure - pursuit guidance law .daly et al . developed a landing controller for a quad - rotor which can hover and land on a moving vehicle .however , landing using a fixed - wing aerial vehicle instead of a quad - rotor onto a moving vehicle is much more challengeable .another relevant literature is the rendezvous / landing guidance with impact angle constraints where the impact angle is the angle about which the landing or rendezvous takes place . in those works ,the trajectories are not optimized .the contributions of this paper are as follows .first , we propose an optimization - based strategy for the generation of optimal uav rendezvous trajectory onto a moving ugv . in order to generate realistic rendezvous trajectories, the strategy has to take dynamics and kinematics of the uav and ugv into account .the coupled uav - ugv dynamics and the constraints arising from the rendezvous maneuver make the design of the strategy complex .we set up the rendezvous optimal control problem in terms of a suitable error dynamics which describe the coupled dynamics .the error dynamics make the analysis and design of the rendezvous strategy simpler , because the key for achieving successful rendezvous is that the error coordinates are zero at the rendezvous point .second , we identify an aggressiveness index in our rendezvous optimal control problem which allows us to control the uav rendezvous behavior .the aggressiveness index is based on the performance limitations of the uav ( i.e. , the constraint limits on the state , input variables ) , thus allowing us to compute aggressive trajectories ( several dynamic constraints are active while the uav is approaching the ugv ) or very smooth ones .the proposed optimal solution framework for the uav - ugv rendezvous can be seen as a framework which allows one to select ( in form of tuning knob ) the type of uav trajectory . finally ,through numerical computations , we show the effectiveness of our approach and discuss a set of interesting features of the rendezvous trajectories .the rest of the paper is organized as follows . in section [ sec : pf ] , we propose the optimal control formulation for the uav - ugv rendezvous . in section[ sec : solution ] , we describe the optimal control based strategy for effectively solving the rendezvous optimal control problem . this technique is evaluated through numerical computations and illustrated in section [ sec : results ] .the conclusions are given in section [ sec : conclude ] ..nomenclature [ cols= " < , < " , ]   [ table : nomenclature ]in this section , we address the rendezvous problem of a fixed - wing uav onto a moving ugv .we first introduce the equations of motion for uav and ugv , and outline the constraints .second , we describe the uav and ugv dynamics with respect to a suitable error dynamics ( i.e. , the velocity frame of the ugv ) . we then formulate the rendezvous problem with respect to the coupled uav - ugv dynamics . in table[ table : nomenclature ] we provide a list of the symbols used in the paper .we use a 3d point mass model for the aerial vehicle .the six dof equations of motion can be written as where , and .the airspeed , , and the ground speed , , are related by where , and are the wind components in the inertial frame . exploiting the wind triangle ,see figure [ fig : windtriangle ] , the airspeed , the heading angle , and the air - mass - referenced flight path angle are given by  we consider three control inputs for the uav : , , and .in particular , we vary the thrust of the vehicle to affect the airspeed of the uav .the is the roll rate by which the uav heading angle and the flight path angle are updated .the is the lift coefficient which we assume to operate in the linear region and hence approximately a linear function of the angle of attack  .  the uavs have state and input constraints . in particular , the airspeed , , the load factor , , and the flight path angle , , are bounded by and , and , and , respectively .the thrust is constrained to be positive and less than the maximum value .moreover , the roll angle , the roll rate , and the lift coefficient are bounded in module by , , , respectively .more specifically , the following state and input constraints are imposed on the model : the uav parameters , aerodynamic coefficients and the constraint parameters used in the paper are given in appendix .we model the ugv as a 2d point mass model  . in this case , the equations of motion are we recall that the ugv can move on a pre - determined path as the one shown in figure [ fig : scenario2 ] .therefore , we take the control input of the ugv to be the longitudinal acceleration , . the lateral acceleration can be written as , where is the ( fixed ) path curvature  .note that we describe the ugv curvature as a function of the path coordinate ( or arc length coordinate ) .in other words , the ugv can accelerate / decelerate along the fixed path defined by the curvature .  due to the tire - road force interaction ,the vehicle acceleration is limited by the so called friction circle ( more generally friction ellipse )  . here ,we take into account a circular acceleration constraint : the acceleration has to be less than or equal to , i.e. ,    the coordinates of the aerial vehicle expressed in the inertial frame , ^t ] , as following , see figure [ fig : new_coord_3d ] ,      where ^t ] . by differentiating with respect to the time , we get   \dot{\chi}_{g } e  + r_z({\chi}_{g } ) \dot{e}\,.\ ] ] we substitute the kinematics of both the vehicle models , equations  and  in equation , that results in that is now it is straightforward to compute the expression of as equation describes the kinematic position error of the uav with respect to the ugv .defining the course angle error as , the speed error as , the flight path error as , and the roll error as , the coupled nonlinear system , , can be written with respect to the new set of coordinates as given the coupled uav - ugv dynamics  and the constraints  and , we introduce two additional constraints .first , the vertical error coordinate , , must be semi - negative . in other words, we are avoiding uav collision with the ground ( since the ugv altitude is zero ) .second , for the physical docking at the rendezvous point , we define the rendezvous constraint based on the course angle error . at the rendezvous point ( i.e. , when the kinematic error components , , , , are zero ) the course angle error has to be less than a given tolerance , .specifically , the following two constraints are taken into account :  [ sys : dockingconstraints ]   due to the presence of the error coordinates in the right hand side of , if the uav is far away from the ugv , the course angle error is bounded by a large positive number and the constraint is relaxed . in other words , the rendezvous constraint does not affect the uav behavior when the uav and ugv are far away each other .this constraint formulation allows us to guide the uav to the ugv for the successful rendezvous thus avoiding the uav approaching the ugv in a perpendicular direction .we now formulate the rendezvous problem with respect to the coupled uav - ugv dynamics .motivated by the application scenario depicted in figure [ fig : scenario2 ] , we assume that the path of the ugv and the time interval for rendezvous are given . specifically , the ugv can move along a fixed path based on the specific scenario ( e.g. , a pre - determined area is assigned for docking or landing task ) .the time interval for rendezvous enables the ugv to create a schedule for service different vehicles operating in the same area . for this purpose, the uav must land onto the ugv between a given time interval  ] , where defines the maximum space for the execution of the rendezvous maneuver .let be the desired space for the rendezvous maneuver , such that . within the rendezvous space interval ] is the aggressiveness index .the flight path angle for aggressiveness index equals to zero , i.e. , , is obtained by imposing the successful execution of the rendezvous maneuver at the maximum space  ] ) which allows one to control the aggressiveness of the uav trajectory .now , with the desired curve in hand , we design the initial trajectory to initialize ` pronto ` as follows .the uav is in forward flight , constant - altitude flight equal to , and constant speed profile equal to the initial speed .the ugv is traveling along the pre - determined path with constant speed equal to .given the initial uav and ugv trajectories , the initial trajectory for the coupled uav - ugv dynamics ( i.e. , it satisfies ) is obtained by using .we highlight that the desired curve is not a trajectory ( it does not satisfied the coupled uav - ugv dynamics ) whereas the initial trajectory is a non - aggressive maneuver , which is easy to compute .this is an important point of the strategy .the desired curve is in fact a guess and we leave ` pronto ` to take care of the dynamics and state - input constraints and thus compute a trajectory ( i.e. , satisfying the uav - ugv dynamics ) .we illustrate the proposed uav - ugv rendezvous strategy using numerical computations .we start with a relatively simple benchmark scenario : the uav is landing onto the ugv which is moving along a straight line path .then , motivated by the scenario in figure [ fig : scenario2 ] , we take into account a turn for the ugv path : the strong coupling between longitudinal and lateral dynamics of both uav and ugv makes the computations particularly challenging and allows us to strengthen the results . for both scenarios ,the rendezvous maneuver starts at .the initial ground speed is m/s and the final rendezvous speed is set to .we assume planar wind field with wind components .it is worth noting that , differently from the approach proposed in  , we do not tune the terms in the weighing matrices ( they are the same for all the computations ) . in order to control the aggressivness of the ( local ) optimal trajectory ,we modify only one parameter , i.e. , the aggressiveness index .the initial position of the uav is , the orientation is , flight angle and roll angle are , , respectively .the initial position and orientation of the ugv are , and , respectively .the maximum space for the execution of the rendezvous maneuver is m . we run ` pronto ` based on the rendezvous trajectory generation strategy for aggressiveness index equals to .we obtain a quadratic convergence rate in the neighbourhood of the solution ( we recall that the ` pronto ` has a structure of a standard newton method ) at each iteration of the algorithm .the local optimal trajectory is shown in figures [ fig : straightlinepathk0_path ] and [ fig : straightlinek0 ] .  in figure[ fig : straightlinepathk0_path ] we show the ( local ) optimal 3d path traversed by the uav to rendezvous with the ugv .the ( local ) optimal uav path is soft : the uav height is reduced gradually .this soft feature is also evident from the trajectory shown in figure [ fig : straightlinek0 ] .in fact , the vertical error coordinate and the flight path angle vary smoothly , figures [ fig : straightlinepathk0_ez ] and [ fig : straightlinepathk0_gam ] , and the constraints on thrust , flight path angle , coefficient lift , and normal load are never active , figures [ fig : straightlinepathk0_u1 ] , [ fig : straightlinepathk0_gam ] , [ fig : straightlinepathk0_cl ] , [ fig : straightlinepathk0_nlf ] .we observe that the ( local ) optimal thrust is different from the desired one , see figure [ fig : straightlinepathk0_u1 ] .such a difference is due to the fact that the desired curve is based on trim conditions ( i.e. , speed transition in forward flight and constant altitude , see ) and , thus , does not take into account the change in the flight altitude as well as important dynamic features . finally , we highlight that the rendezvous time is ( note that m for , see figure [ fig : straightlinezcomparisonk000 ] ) and the desired rendezvous time is , see .  : ( local ) optimal path .the blue and green lines represent the ugv and the uav paths , respectively . , width=302 ]  next , we run the rendezvous trajectory generation strategy for aggressiveness index equals to and we compare the ( local ) optimal trajectories in figure [ fig : straightlinepathcomparisonk ] ( for the sake of completeness , we include the rendezvous trajectory obtained with ) . for ( local ) optimal uav path ( blue line in figure [ fig : straightlinepathcomparisonk_ez ] ) is aggressive . by aggressive , we mean that the several constraints are active during the rendezvous maneuver .indeed , the thrust is zero for almost all the rendezvous maneuver , figure [ fig : straightlinepathcomparisonk_u1 ] , and the constraint on the normal load is active at the beginning of the maneuver , figure [ fig : straightlinepathcomparisonk_nlf ] .moreover , we observe a ( relative ) high speed error during the maneuver , figure [ fig : straightlinepathcomparisonk_ev ] .such a difference in the ground speed between the uav and the ugv is due to the wind ( which affects only the uav ) and the fact that the airspeed is constrained .next , we highlight two interesting features of the ( local ) optimal trajectory for .first , at the beginning of the rendezvous maneuver , the uav decreases the thrust and , at the same time , increases the lift coefficient ( see the kink at about sec in figure [ fig : straightlinepathcomparisonk_cl ] , blue line ) .in this way , the airspeed decreases at about and , immediately after , increases thus reaching its maximum value .such aggressive maneuver allows the uav to take a steep dive towards the ugv as shown in figure [ fig : straightlinepathcomparisonk_ez ] .second , once the uav ground - speed reaches the desired value of ( i.e. , ) , the uav needs to maintain this speed and hence it requires thrust which is increased from zero to the desired value as shown in the figures [ fig : straightlinepathcomparisonk_u1 ] .similar behavior is observed in the lift coefficient , figure [ fig : straightlinepathcomparisonk_cl ] .such a sharp variation in the thrust and lift coefficient highlights an important transient behavior at the end of the rendezvous maneuver : the vertical error coordinate reaches the desired value without overshooting , thus ensuring the feasibility of the trajectory ( i.e. , it satisfies the constraints ) , see figure [ fig : straightlinepathcomparisonk_ez ] and the zoom in figure [ fig : straightlinezcomparisonk100 ] at about .  finally , the sequence of rendezvous time is , , , for , respectively . comparing the rendezvous time with the desired one predicted by , we observe a good matching expect for the case .in fact , due to the transient behavior at the end of the aggressive maneuver , the optimal rendezvous time is ( note that for , see figure [ fig : straightlinezcomparisonk100 ] ) , yet the desired rendezvous time is .   in this scenario ,the ugv is moving along a circuit as the one mentioned in the introduction .in particular , we take into account a section of the circuit shown in figure [ fig : scenario2 ] which is composed by turn with a radius of m and straights of m before and after the turn , see figure [ fig:90degpath ] .  . ,width=340 ]  the initial position of the uav is , the orientation is , and flight angle and roll angle are , , respectively .the initial position and orientation of the ugv are and , respectively .we run the rendezvous trajectory generation strategy for aggressiveness index equals to and we compare the ( local ) optimal trajectories in figures [ fig:90degpath ] and [ fig:90deg_k ] .  as in the previous computations , we are able to control the aggressiveness of the uav trajectorythus , for ( blue line in figures [ fig:90degpath ] and [ fig:90deg_k ] ) several constraints are active . for ,the uav height is reduced gradually thus highlighting the soft feature of the local optimal trajectory ( green line in figures [ fig:90degpath ] and [ fig:90deg_k ] ) .it is worth highlighting the effect of the right turn on the rendezvous maneuver . in order to minimize the lateral error coordinate, the uav turns by rolling , see figure [ fig:90degk1_ph ] .however , the uav is not able to track exactly the ugv .the lateral error coordinate is no zero and the constraint on the roll angle is never active , see figures [ fig:90degk1_ey ] and [ fig:90degk1_ph ] .this is due to the fact that the constraint on the load factor becomes active ( see figure [ fig:90deg_k_ez_nlf ] ) before the roll angle reaches its maximum value . indeed , in constant descent flight conditions ( i.e. , and ), the lift must be equal to and the load factor becomes .it is evident that the roll angle is constrained by which turns out to be less than .this explains the no - zero lateral error coordinate .this computation allows us to highlight the coupled uav - ugv dynamics .indeed , for , the uav roll reaches ( as discussed before , its maximum value ) and the ugv lateral acceleration is at the maximum value , , at exactly the same time , see figure [ fig:90degk1_ph ] and [ fig:90degk1_acar ] , respectively . finally , although the desired curve is based on the decoupled uav - ugv dynamics , we are able to predict the rendezvous time .the sequence of rendezvous time is , , , , for , respectively , as predicted by .in this paper we proposed an optimal control approach for the refueling problem of fixed - wing uavs using a ugv as a refueling unit .we provided a rigourous optimal control problem formulation for uav rendezvous with the moving ugv and we addressed the optimal control problem by using a trajectory - tracking approach . based on a nonlinear optimal control solver , we proposed an optimal control based strategy which allows us to compute optimal feasible trajectories for both uav and ugv . by changing the aggressiveness index in our proposed strategy , we are able to compute aggressive trajectories ( i.e. , several constraints are active while the uav is approaching the ugv ) or very smooth ones .a key property of the proposed approach is that we are able to predict and , therefore , select ( in form of tuning knob ) the time to rendezvous , which is an important performance feature of the uav trajectory .we provided numerical computations showing the effectiveness of the proposed approach .future directions of research will include field tests where the obtained optimal trajectories are feed as reference trajectories to the trajectory tracking algorithms that are running on the vehicles to perform the rendezvous task .[ sec : appendix ] the uav parameters are based on the `` zagi '' flying wing  :  we assume that the air density is constant and equal to [kg / m . the minimum and maximum airspeed , normal load , maximum thrust , roll angle , and coefficient lift are set as follows   the maximum acceleration of the ugv is 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Abstract: fixed - wind unmanned aerial vehicles ( uavs ) are essential for low cost aerial surveillance and mapping applications in remote regions . one of the main limitations of uavs is limited fuel capacity and hence requires periodic refueling to accomplish a mission . the usual mechanism of commanding the uav to return to a stationary base station for refueling can result in fuel wastage and inefficient mission operation time . alternatively , unmanned gound vehicle ( ugv ) can be used as a mobile refueling unit where the uav will rendezvous with the ugv for refueling . in order to accurately perform this task in the presence of wind disturbances , we need to determine an optimal trajectory in 3d taking uav and ugv dynamics and kinematics into account . in this paper , we propose an optimal control formulation to generate a tunable uav trajectory for rendezvous on a moving ugv taking wind disturbances into account . by a suitable choice of the value of an aggressiveness index in our problem setting , we are able to control the uav rendezvous behavior . several numerical results are presented to show the reliability and effectiveness of our approach .