Tools for quantum network design

Quantum networks will enable the implementation of communication tasks with qualitative advantages with respect to the communication networks we know today. While it is expected that the first demonstrations of small scale quantum networks will take place in the near term, many challenges remain to scale them. To compare different solutions, optimize over parameter space and inform experiments, it is necessary to evaluate the performance of concrete quantum network scenarios. Here, we review the state of the art of tools for evaluating the performance of quantum networks. We present them from three different angles: information-theoretic benchmarks, analytical tools, and simulation.

[1]  Franck Cappello,et al.  Full-state quantum circuit simulation by using data compression , 2019, SC.

[2]  R. Chaves,et al.  Statistical Properties of the Quantum Internet. , 2019, Physical review letters.

[3]  Stefan Bäuml,et al.  Universal limitations on quantum key distribution over a network , 2019, ArXiv.

[4]  Mark M. Wilde,et al.  Squashed entanglement and approximate private states , 2016, Quantum Inf. Process..

[5]  Michael Epping,et al.  Large-scale quantum networks based on graphs , 2015, 1504.06599.

[6]  Martin Rötteler,et al.  Perfect quantum network communication protocol based on classical network coding , 2009, 2010 IEEE International Symposium on Information Theory.

[7]  Joseph D. Touch,et al.  Designing quantum repeater networks , 2013, IEEE Communications Magazine.

[8]  M. Horodecki,et al.  General teleportation channel, singlet fraction and quasi-distillation , 1998, quant-ph/9807091.

[9]  Koji Azuma,et al.  Fundamental limitation on quantum broadcast networks , 2016, 1609.03994.

[10]  Suguru Arimoto,et al.  An algorithm for computing the capacity of arbitrary discrete memoryless channels , 1972, IEEE Trans. Inf. Theory.

[11]  Saikat Guha,et al.  The Squashed Entanglement of a Quantum Channel , 2013, IEEE Transactions on Information Theory.

[12]  Axel Dahlberg,et al.  How to transform graph states using single-qubit operations: computational complexity and algorithms , 2018, Quantum Science and Technology.

[13]  Siddhartha Santra,et al.  Quantum repeater architecture with hierarchically optimized memory buffer times , 2018, Quantum Science and Technology.

[14]  Louis Petingi,et al.  Packing the Steiner trees of a graph , 2009 .

[15]  V. Buzek,et al.  Quantum secret sharing , 1998, quant-ph/9806063.

[16]  David Elkouss,et al.  Linear programs for entanglement and key distribution in the quantum internet , 2018, Communications Physics.

[17]  T. Ralph,et al.  Fundamental building block for all-optical scalable quantum networks , 2018, Physical Review A.

[18]  Baochun Li,et al.  Network Coding : The Case of Multiple Unicast Sessions , 2004 .

[19]  Ying Li,et al.  Long range failure-tolerant entanglement distribution , 2013 .

[20]  Nilanjana Datta,et al.  Min- and Max-Relative Entropies and a New Entanglement Monotone , 2008, IEEE Transactions on Information Theory.

[21]  Rajkumar Kettimuthu,et al.  Simulations of Photonic Quantum Networks for Performance Analysis and Experiment Design , 2019, 2019 IEEE/ACM Workshop on Photonics-Optics Technology Oriented Networking, Information and Computing Systems (PHOTONICS).

[22]  Stenio F. L. Fernandes,et al.  Performance Evaluation for Network Services, Systems and Protocols , 2017, Springer International Publishing.

[23]  Qiaoyan Wen,et al.  Object-Oriented Quantum Cryptography Simulation Model , 2007, Third International Conference on Natural Computation (ICNC 2007).

[24]  Jeroen van de Graaf,et al.  Cryptographic Distinguishability Measures for Quantum-Mechanical States , 1997, IEEE Trans. Inf. Theory.

[25]  Michele Amoretti,et al.  Entanglement Verification in Quantum Networks With Tampered Nodes , 2020, IEEE Journal on Selected Areas in Communications.

[26]  Peter Elias,et al.  A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.

[27]  Nicolas Gisin,et al.  Quantum repeaters based on atomic ensembles and linear optics , 2009, 0906.2699.

[28]  Peter van Loock,et al.  3/4-Efficient Bell measurement with passive linear optics and unentangled ancillae. , 2014, Physical review letters.

[29]  J. Cirac,et al.  Long-distance quantum communication with atomic ensembles and linear optics , 2001, Nature.

[30]  P. Kok,et al.  Statistical analysis of quantum-entangled-network generation , 2018, Physical Review A.

[31]  Maor Ganz,et al.  Quantum leader election , 2009, Quantum Inf. Process..

[32]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[33]  Norbert Lütkenhaus,et al.  Ultrafast and fault-tolerant quantum communication across long distances. , 2013, Physical review letters.

[34]  W. Dur,et al.  Two-dimensional quantum repeaters , 2016, 1604.05352.

[35]  Frank Harary,et al.  Graph Theory , 2016 .

[36]  Hermann Kampermann,et al.  Quantum repeaters and quantum key distribution: Analysis of secret-key rates , 2012, 1208.2201.

[37]  Richard E. Blahut,et al.  Computation of channel capacity and rate-distortion functions , 1972, IEEE Trans. Inf. Theory.

[38]  Matthias Kriesell,et al.  Edge-disjoint trees containing some given vertices in a graph , 2003, J. Comb. Theory, Ser. B.

[39]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[40]  Sina Salek,et al.  Enhanced Communication with the Assistance of Indefinite Causal Order. , 2017, Physical review letters.

[41]  Hoi-Kwong Lo,et al.  Fundamental rate-loss trade-off for the quantum internet , 2016, Nature Communications.

[42]  Yuval Rabani,et al.  An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm , 1998, SIAM J. Comput..

[43]  Stefano Pirandola,et al.  End-to-end capacities of a quantum communication network , 2019, Communications Physics.

[44]  Iordanis Kerenidis,et al.  Shortcuts to quantum network routing , 2015, ArXiv.

[45]  W. Munro,et al.  From quantum multiplexing to high-performance quantum networking , 2010 .

[46]  H. Raedt,et al.  Event-by-event Simulation of Quantum Cryptography Protocols ∗ , 2007, 0708.1734.

[47]  D Cavalcanti,et al.  Distribution of entanglement in large-scale quantum networks , 2012, Reports on progress in physics. Physical Society.

[48]  Stefan Rass,et al.  Implementation of quantum key distribution network simulation module in the network simulator NS-3 , 2017, Quantum Information Processing.

[49]  Takaaki Matsuo,et al.  Simulation of a Dynamic, RuleSet-based Quantum Network , 2019, ArXiv.

[50]  Wolfgang Dür,et al.  Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication , 1998 .

[51]  Donald F. Towsley,et al.  On the Capacity Region of Bipartite and Tripartite Entanglement Switching , 2019, SIGMETRICS Perform. Evaluation Rev..

[52]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.

[53]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[55]  Hiroshi Esaki,et al.  Protocol design for quantum repeater networks , 2011, AINTEC '11.

[56]  A. Winter,et al.  “Squashed entanglement”: An additive entanglement measure , 2003, quant-ph/0308088.

[57]  Peter van Loock,et al.  Ultrafast fault-tolerant long-distance quantum communication with static linear optics , 2016, 1610.04519.

[58]  Debbie W. Leung,et al.  Quantum Network Communication—The Butterfly and Beyond , 2010, IEEE Transactions on Information Theory.

[59]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[60]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[61]  Stefano Pirandola Bounds for multi-end communication over quantum networks , 2019 .

[62]  A. Fowler,et al.  Surface code quantum communication. , 2009, Physical review letters.

[63]  Ekert,et al.  "Event-ready-detectors" Bell experiment via entanglement swapping. , 1993, Physical review letters.

[64]  S. K. Subramaniam,et al.  An efficient modeling and simulation of quantum key distribution protocols using OptiSystem™ , 2012, 2012 IEEE Symposium on Industrial Electronics and Applications.

[65]  Rafael Chaves,et al.  Semidefinite Tests for Quantum Network Topologies. , 2020, Physical review letters.

[66]  Iordanis Kerenidis,et al.  Practical Quantum Coin Flipping , 2011 .

[67]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[68]  Michal Horodecki,et al.  Long-distance quantum communication over noisy networks without long-time quantum memory , 2012 .

[69]  Stephen J. Wright Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[70]  B. Valiron,et al.  Quantum computations without definite causal structure , 2009, 0912.0195.

[71]  Robert R.Tucci Entanglement of Distillation and Conditional Mutual Information , 2002 .

[72]  Mohammad R. Salavatipour,et al.  Hardness and approximation results for packing steiner trees , 2005, Algorithmica.

[73]  S. Guha,et al.  Fundamental rate-loss tradeoff for optical quantum key distribution , 2014, Nature Communications.

[74]  Lap Chi Lau,et al.  An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem* , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

[75]  David Elkouss,et al.  Efficient Optimization of Cut-offs in Quantum Repeater Chains , 2020, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE).

[76]  Saikat Guha,et al.  On the Stochastic Analysis of a Quantum Entanglement Distribution Switch , 2019, IEEE Transactions on Quantum Engineering.

[77]  Travis S. Humble,et al.  Programmable multi-node quantum network design and simulation , 2016, SPIE Commercial + Scientific Sensing and Imaging.

[78]  W. Dur,et al.  Modular architectures for quantum networks , 2017, 1711.02606.

[79]  Martin Rötteler,et al.  Constructing quantum network coding schemes from classical nonlinear protocols , 2010, 2011 IEEE International Symposium on Information Theory Proceedings.

[80]  Koji Azuma,et al.  Aggregating quantum repeaters for the quantum internet , 2016, 1606.00135.

[81]  Holger Boche,et al.  Extending Quantum Links: Modules for Fiber‐ and Memory‐Based Quantum Repeaters , 2019, Advanced Quantum Technologies.

[82]  Rodney Van Meter,et al.  Quantum link bootstrapping using a RuleSet-based communication protocol , 2019, Physical Review A.

[83]  Ben Bartlett,et al.  A distributed simulation framework for quantum networks and channels , 2018, 1808.07047.

[84]  W. Munro,et al.  Hybrid quantum repeater using bright coherent light. , 2005, Physical Review Letters.

[85]  C. Simon,et al.  Quantum repeaters with individual rare-earth ions at telecommunication wavelengths , 2017, Quantum.

[87]  Pawel Horodecki,et al.  Multipartite secret key distillation and bound entanglement , 2008, 0811.3603.

[88]  Masterarbeit von Alexander Müller-Hermes Transposition in Quantum Information Theory , 2012 .

[89]  T. C. Hu Multi-Commodity Network Flows , 1963 .

[90]  Antonio Acín,et al.  Quantum Inflation: A General Approach to Quantum Causal Compatibility , 2019, Physical Review X.

[91]  Marek Sawerwain,et al.  Quantum Router for Qutrit Networks , 2020, CN.

[92]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[93]  A Kuzmich,et al.  Multiplexed memory-insensitive quantum repeaters. , 2007, Physical review letters.

[94]  Axel Dahlberg,et al.  Transforming graph states using single-qubit operations , 2018, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[95]  Nicolas J Cerf,et al.  No-go theorem for gaussian quantum error correction. , 2008, Physical review letters.

[96]  David Elkouss,et al.  Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains , 2019, IEEE Journal on Selected Areas in Communications.

[97]  F. Grosshans,et al.  Ancilla-assisted linear optical Bell measurements and their optimality , 2018, Physical Review A.

[98]  Averill M. Law,et al.  How to build valid and credible simulation models , 2008, 2008 Winter Simulation Conference.

[99]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[100]  W. Munro,et al.  Inside Quantum Repeaters , 2015, IEEE Journal of Selected Topics in Quantum Electronics.

[101]  Michael Epping,et al.  Robust entanglement distribution via quantum network coding , 2016 .

[102]  P. Kok,et al.  Practical repeaters for ultralong-distance quantum communication , 2016, 1607.08140.

[103]  Yi-Wei Shi,et al.  Solving Quantum Channel Discrimination Problem With Quantum Networks and Quantum Neural Networks , 2019, IEEE Access.

[104]  Alexander Semenovich Holevo,et al.  Quantum Systems, Channels, Information: A Mathematical Introduction , 2019 .

[105]  M. Lewenstein,et al.  Quantum Entanglement , 2020, Quantum Mechanics.

[106]  W. Dur,et al.  Measurement-based quantum repeaters , 2012, 1204.2178.

[107]  M. Koashi,et al.  Quantum repeaters and computation by a single module: Remote nondestructive parity measurement , 2010, 1003.0181.

[108]  David Elkouss,et al.  Entanglement Distribution in a Quantum Network: A Multicommodity Flow-Based Approach , 2020, IEEE Transactions on Quantum Engineering.

[109]  Koji Azuma,et al.  Versatile relative entropy bounds for quantum networks , 2017, 1707.05543.

[110]  H. Zimmermann,et al.  OSI Reference Model - The ISO Model of Architecture for Open Systems Interconnection , 1980, IEEE Transactions on Communications.

[111]  Sumeet Khatri,et al.  Policies for elementary link generation in quantum networks , 2020, ArXiv.

[112]  Li Zhou,et al.  Protocols for Packet Quantum Network Intercommunication , 2019, IEEE Transactions on Quantum Engineering.

[113]  Edo Waks,et al.  Serialized quantum error correction protocol for high-bandwidth quantum repeaters , 2015, 1508.05966.

[114]  C. Branciard,et al.  Communication through coherent control of quantum channels , 2018, Quantum.

[115]  Tristan Kraft,et al.  Characterizing quantum networks: Insights from coherence theory , 2020, Physical Review A.

[116]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[117]  Hermann Kampermann,et al.  Measurement-device-independent quantum key distribution with quantum memories , 2013, 1306.3095.

[118]  P. Loock,et al.  Memory-assisted long-distance phase-matching quantum key distribution , 2019, 1910.03333.

[119]  Prasanta K. Panigrahi,et al.  Quantum cheques , 2016, Quantum Inf. Process..

[120]  H. Briegel,et al.  Entanglement purification and quantum error correction , 2007, 0705.4165.

[121]  Robert König,et al.  Universally Composable Privacy Amplification Against Quantum Adversaries , 2004, TCC.

[122]  Kae Nemoto,et al.  Quantum communication without the necessity of quantum memories , 2012, Nature Photonics.

[123]  Saikat Guha,et al.  Rate-distance tradeoff and resource costs for all-optical quantum repeaters , 2016, Physical Review A.

[124]  Mihalis Yannakakis,et al.  Primal-dual approximation algorithms for integral flow and multicut in trees , 1997, Algorithmica.

[125]  Bart De Moor,et al.  Graphical description of the action of local Clifford transformations on graph states , 2003, quant-ph/0308151.

[126]  J. Cirac,et al.  Quantum repeaters based on entanglement purification , 1998, quant-ph/9808065.

[127]  J. M. Taylor,et al.  Fast and robust approach to long-distance quantum communication with atomic ensembles , 2006, quant-ph/0609236.

[128]  Viacheslav V. Kuzmin,et al.  Diagrammatic technique for simulation of large-scale quantum repeater networks with dissipating quantum memories , 2020, 2009.10415.

[129]  David Elkouss,et al.  NetSquid, a discrete-event simulation platform for quantum networks , 2020 .

[130]  André Bouchet,et al.  Graphic presentations of isotropic systems , 1987, J. Comb. Theory, Ser. B.

[131]  J. Eisert,et al.  Quantum network routing and local complementation , 2018, npj Quantum Information.

[132]  Jennifer L. Barry,et al.  Quantum partially observable Markov decision processes , 2014 .

[133]  Michal Horodecki,et al.  General Paradigm for Distilling Classical Key From Quantum States , 2009, IEEE Transactions on Information Theory.

[134]  W. Grice Arbitrarily complete Bell-state measurement using only linear optical elements , 2011 .

[135]  F. Schmidt,et al.  Waiting time in quantum repeaters with probabilistic entanglement swapping , 2017, Physical Review A.

[136]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[137]  Optimising repeater schemes for the quantum internet , 2020 .

[138]  Petteri Kaski,et al.  Packing Steiner trees with identical terminal sets , 2004, Inf. Process. Lett..

[139]  S. Wehner,et al.  Quantum internet: A vision for the road ahead , 2018, Science.

[140]  N. Lütkenhaus,et al.  Maximum efficiency of a linear-optical Bell-state analyzer , 2001 .

[141]  A. Sørensen,et al.  Memory imperfections in atomic-ensemble-based quantum repeaters , 2008, 0803.2069.

[142]  András Varga,et al.  An overview of the OMNeT++ simulation environment , 2008, SimuTools.

[143]  Peter van Loock,et al.  Rate analysis for a hybrid quantum repeater , 2010, 1010.0106.

[144]  A. Zeilinger,et al.  Going Beyond Bell’s Theorem , 2007, 0712.0921.

[145]  Hoi-Kwong Lo,et al.  All-photonic quantum repeaters , 2013, Nature Communications.

[146]  Peter van Loock,et al.  Ultrafast Long-Distance Quantum Communication with Static Linear Optics. , 2015, Physical review letters.

[147]  Leandros Tassiulas,et al.  Routing entanglement in the quantum internet , 2017, npj Quantum Information.

[148]  Giulio Chiribella,et al.  Quantum Shannon theory with superpositions of trajectories , 2018, Proceedings of the Royal Society A.

[149]  Stephanie Wehner,et al.  A Quantum Router Architecture for High-Fidelity Entanglement Flows in Multi-User Quantum Networks , 2020 .

[150]  Kae Nemoto,et al.  A ug 2 00 8 A high bandwidth quantum repeater , 2008 .

[151]  Michele Amoretti,et al.  Enhancing distributed functional monitoring with quantum protocols , 2019, Quantum Information Processing.

[152]  M. Lukin,et al.  One-Way Quantum Repeater Based on Near-Deterministic Photon-Emitter Interfaces , 2019, Physical Review X.

[153]  Alexander Pirker,et al.  Genuine quantum networks with superposed tasks and addressing , 2020, npj Quantum Information.

[154]  Jack L. Burbank,et al.  An Introduction to Network Modeling and Simulation for the Practicing Engineer (The ComSoc Guides to Communications Technologies) , 2011 .

[155]  Jacob M. Taylor,et al.  Quantum repeater with encoding , 2008, 0809.3629.

[156]  Marcin Niemiec,et al.  Quantum Cryptography Protocol Simulator , 2011, MCSS.

[157]  Michael Epping,et al.  Multi-partite entanglement can speed up quantum key distribution in networks , 2016, 1612.05585.

[158]  Hongyi Zhou,et al.  Security assessment and key management in a quantum network , 2019, ArXiv.

[159]  D. Gottesman,et al.  Longer-baseline telescopes using quantum repeaters. , 2011, Physical review letters.

[160]  Jing Wang,et al.  Quantum Secured Internet Transport , 2020, Information Systems Frontiers.

[161]  Janis Noetzel,et al.  QuNetSim: A Software Framework for Quantum Networks , 2020, ArXiv.

[162]  M. Kafatos Bell's theorem, quantum theory and conceptions of the universe , 1989 .

[163]  David Avis,et al.  Distributed compression and multiparty squashed entanglement , 2007, ArXiv.

[164]  Salman Beigi,et al.  Genuine Quantum Nonlocality in the Triangle Network. , 2019, Physical review letters.

[165]  Bernardo A. Huberman,et al.  A Quantum Router For The Entangled Web , 2019, Inf. Syst. Frontiers.

[166]  Joseph Fitzsimons,et al.  Composable Security of Delegated Quantum Computation , 2013, ASIACRYPT.

[167]  M. Christandl,et al.  Relative Entropy Bounds on Quantum, Private and Repeater Capacities , 2016, Communications in Mathematical Physics.

[168]  Michael R. Grimaila,et al.  A Modeling Framework for Studying Quantum Key Distribution System Implementation Nonidealities , 2015, IEEE Access.

[169]  A. Pereszlenyi,et al.  Simulation of quantum key distribution with noisy channels , 2005, Proceedings of the 8th International Conference on Telecommunications, 2005. ConTEL 2005..

[170]  Dong Jin,et al.  SeQUeNCe: a customizable discrete-event simulator of quantum networks , 2020, Quantum Science and Technology.

[171]  Some Sankar Bhattacharya,et al.  Indefinite causal order enables perfect quantum communication with zero capacity channels , 2018, New Journal of Physics.

[172]  Mihalis Yannakakis,et al.  Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications , 1996, SIAM J. Comput..

[173]  K. Menger Zur allgemeinen Kurventheorie , 1927 .

[174]  Mark M. Wilde,et al.  Bounds on Entanglement Distillation and Secret Key Agreement for Quantum Broadcast Channels , 2015, IEEE Transactions on Information Theory.

[175]  M. Lukin,et al.  Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters , 2005, quant-ph/0502112.

[176]  L. Banchi,et al.  Fundamental limits of repeaterless quantum communications , 2015, Nature Communications.

[177]  Klaus Wehrle,et al.  Modeling and Tools for Network Simulation , 2010, Modeling and Tools for Network Simulation.

[178]  Stephanie Wehner,et al.  Designing a quantum network protocol , 2020, CoNEXT.

[179]  J. Oppenheim,et al.  Secure key from bound entanglement. , 2003, Physical Review Letters.

[180]  Travis S. Humble,et al.  OpenFlow arbitrated programmable network channels for managing quantum metadata , 2015, The Journal of Defense Modeling and Simulation: Applications, Methodology, Technology.

[181]  S. Pirandola Capacities of repeater-assisted quantum communications , 2016, 1601.00966.

[182]  Axel Dahlberg,et al.  Distributed Routing in a Quantum Internet , 2019, ArXiv.

[183]  Reposition time in probabilistic imperfect memories , 2013, 1309.3407.

[184]  Dong Yang,et al.  Squashed Entanglement for Multipartite States and Entanglement Measures Based on the Mixed Convex Roof , 2007, IEEE Transactions on Information Theory.

[185]  Rodney Van Meter,et al.  Quantum networking and internetworking , 2012, IEEE Network.

[186]  Bo Yuan,et al.  Classical Simulation of Quantum Supremacy Circuits , 2020, 2005.06787.

[187]  Raymond Laflamme,et al.  Concatenated Quantum Codes , 1996 .

[188]  Norbert Lütkenhaus,et al.  Optimal architectures for long distance quantum communication , 2015, Scientific Reports.

[189]  M. Wolf,et al.  Quantum capacities of bosonic channels. , 2006, Physical review letters.

[190]  dek,et al.  Parameter regimes for a single sequential quantum repeater , 2018 .

[191]  Axel Dahlberg,et al.  SimulaQron—a simulator for developing quantum internet software , 2017, Quantum Science and Technology.

[192]  Salman Beigi,et al.  Limits on Correlations in Networks for Quantum and No-Signaling Resources. , 2019, Physical review letters.

[193]  David Malone,et al.  Implementing a Quantum Coin Scheme , 2020, 2020 31st Irish Signals and Systems Conference (ISSC).

[194]  Barry C Sanders,et al.  qkdSim: An experimenter's simulation toolkit for QKD with imperfections, and its performance analysis with a demonstration of the B92 protocol using heralded photon , 2019, 1912.10061.

[195]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.

[196]  Julio A. de Oliveira Filho,et al.  A link layer protocol for quantum networks , 2019, SIGCOMM.

[197]  Isaac L. Chuang,et al.  Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations , 1999, Nature.

[198]  Mario Berta,et al.  Converse Bounds for Private Communication Over Quantum Channels , 2016, IEEE Transactions on Information Theory.

[199]  Deutsch,et al.  Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels. , 1996, Physical review letters.

[200]  V. V. Kuzmin,et al.  Scalable repeater architectures for multi-party states , 2019, npj Quantum Information.

[201]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[202]  Akihito Soeda,et al.  Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions , 2017 .

[203]  Jieping Ye,et al.  A quantum network of clocks , 2013, Nature Physics.

[204]  Debbie W. Leung,et al.  The Universal Composable Security of Quantum Key Distribution , 2004, TCC.

[205]  W. Dur,et al.  Role of memory errors in quantum repeaters , 2007 .