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  3. Quantum Information Theory
  • Cited by 235
Publisher:
Cambridge University Press
Online publication date:
February 2017
Print publication year:
2017
Online ISBN:
9781316809976
DOI:
https://doi.org/10.1017/9781316809976
Subjects:
Physics and Astronomy, Computer Science, Cryptography, Cryptology and Coding, Quantum Physics, Quantum Information and Quantum Computation
Information

Book description

Developing many of the major, exciting, pre- and post-millennium developments from the ground up, this book is an ideal entry point for graduate students into quantum information theory. Significant attention is given to quantum mechanics for quantum information theory, and careful studies of the important protocols of teleportation, superdense coding, and entanglement distribution are presented. In this new edition, readers can expect to find over 100 pages of new material, including detailed discussions of Bell's theorem, the CHSH game, Tsirelson's theorem, the axiomatic approach to quantum channels, the definition of the diamond norm and its interpretation, and a proof of the Choi–Kraus theorem. Discussion of the importance of the quantum dynamic capacity formula has been completely revised, and many new exercises and references have been added. This new edition will be welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.

Reviews

'For years, I have been hoping that somebody would write a book on quantum information theory that was clear, comprehensive, and up to date. This is that book. And the second edition is even better than the first.'

Peter Shor - Massachusetts Institute of Technology

'Mark M. Wilde’s Quantum Information Theory is a natural expositor’s labor of love. Accessible to anyone comfortable with linear algebra and elementary probability theory, Wilde’s book brings the reader to the forefront of research in the quantum generalization of Shannon’s information theory. What had been a gaping hole in the literature has been replaced by an airy edifice, scalable with the application of reasonable effort and complete with fine vistas of the landscape below. Wilde’s book has a permanent place not just on my bookshelf but on my desk.'

Patrick Hayden - Stanford University, California

Review of previous edition:‘… [its] clear, thorough, and above all self-contained presentation will aid quantum information researchers in coming up to speed with the latest results in this area of the field. Meanwhile, the familiar setting and language will help classical information theorists who wish to become more acquainted with the quantum aspects of information processing … The presentation is well-structured, making it easy to jump to the desired topic and quickly determine on what that topic depends and how it is used going forward … Quantum Information Theory fills an important gap in the existing literature and will, I expect, help propagate the latest and greatest results in quantum Shannon theory to both quantum and classical researchers.'

Joseph M. Renes Source: Quantum Information Processing

Review of previous edition:‘… a modern self-contained text … suitable for graduate-level courses leading up to research level.'

Source: Journal of Discrete Mathematical Sciences and Cryptography

Review of previous edition:'… the book does a phenomenal job of introducing, developing and nurturing a mathematical sense of quantum information processing … In a nutshell, this is an essential reference for students and researchers who work in the area or are trying to understand what it is that quantum information theorists study. Wilde, as mentioned in his book, beautifully illustrates 'the ultimate capability of noisy physical systems, governed by the laws of quantum mechanics, to preserve information and correlations' through this book. I would strongly recommend it to anyone who plans to continue working in the field of quantum information.'

Subhayan Roy Moulick Source: SIGCAT News

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Contents

Page 1 of 2

Contents

Page 1 of 2

References
References
Abeyesinghe, A (2006), ‘Unification of Quantum Information Theory’, PhD thesis, California Institute of Technology.
Abeyesinghe, A., Devetak, I, Hayden, P & Winter, A (2009), ‘The mother of all protocols: Restructuring quantum information's family tree ’, Proceedings of the Royal Society A 465(2108), 2537–2563. arXiv:quant-ph/0606225.
Abeyesinghe, A & Hayden, P (2003), ‘Generalized remote state preparation: Trading cbits, qubits, and ebits in quantum communication’, Physical Review A 68(6), 062319. arXiv:quant-ph/0308143.
Adami, C & Cerf, N. J (1997), ‘von Neumann capacity of noisy quantum channels’, Physical Review A 56(5), 3470–3483. arXiv:quant-ph/9609024.
Aharonov, D & Ben-Or, M. (1997), ‘Fault-tolerant quantum computation with constant error’, in STOC ‘97: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, ACM, New York, NY, pp. 176–188. arXiv:quant-ph/9906129.
Ahlswede, R & Winter, A (2002), ‘Strong converse for identification via quantum channels’, IEEE Transactions on Information Theory 48(3), 569–579. arXiv:quantph/0012127.
Ahn, C., Doherty, A, Hayden, P & Winter, A (2006), ‘On the distributed compression of quantum information’, IEEE Transactions on Information Theory 52(10), 4349–4357. arXiv:quant-ph/0403042.
Alicki, R & Fannes, M (2004), ‘Continuity of quantum conditional information’, Journal of Physics A: Mathematical and General 37(5), L55–L57. arXiv:quantph/ 0312081.
Araki, H & Lieb, E. H (1970), ‘Entropy inequalities’, Communications in Mathematical Physics 18(2), 160–170.
Aspect, A., Grangier, P & Roger, G (1981), ‘Experimental tests of realistic local theories via Bell's theorem’, Physical Review Letters 47(7), 460–463.
Aubrun, G., Szarek, S & Werner, E (2011), ‘Hastings’ additivity counterexample via Dvoretzky's theorem', Communications in Mathematical Physics 305(1), 85–97. arXiv:1003.4925.
Audenaert, K., De Moor, B, Vollbrecht, K. G. H. & Werner, R. F (2002), ‘Asymptotic relative entropy of entanglement for orthogonally invariant states’, Physical ReviewA 66(3), 032310. arXiv:quant-ph/0204143.
Audenaert, K.M. R. (2007), ‘A sharp continuity estimate for the von Neumann entropy’, Journal of Physics A: Mathematical and Theoretical 40(28), 8127. arXiv:quant-ph/0610146.
Bardhan, B.R., Garcia-Patron, R, Wilde, M. M & Winter, A (2015), ‘Strong converse for the classical capacity of all phase-insensitive bosonic Gaussian channels’, IEEETransactions on Information Theory 61(4), 1842–1850. arXiv:1401.4161.
Barnum, H., Caves, C. M, Fuchs, C. A, Jozsa, R & Schumacher, B (2001), ‘On quantum coding for ensembles of mixed states’, Journal of Physics A: Mathematical and General 34(35), 6767. arXiv:quant-ph/0008024.
Barnum, H., Hayden, P, Jozsa, R & Winter, A (2001), ‘On the reversible extraction of classical information from a quantum source’, Proceedings of the Royal Society A 457(2012), 2019–2039. arXiv:quant-ph/0011072.
Barnum, H & Knill, E (2002), ‘Reversing quantum dynamics with near-optimal quantum and classical fidelity’, Journal of Mathematical Physics 43(5), 2097–2106. arXiv:quant-ph/0004088.
Barnum, H., Knill, E & Nielsen, M. A (2000), ‘On quantum fidelities and channel capacities’, IEEE Transactions on Information Theory 46(4), 1317–1329. arXiv:quant-ph/9809010.
Barnum, H., Nielsen, M. A & Schumacher, B (1998), ‘Information transmission through a noisy quantum channel’, Physical Review A 57(6), 4153–4175.
Beigi, S., Datta, N & Leditzky, F (2015), ‘Decoding quantum information via the Petz recovery map’. arXiv:1504.04449.
Bell, J.S. (1964), ‘On the Einstein–Podolsky–Rosen paradox’, Physics 1, 195–200.
Bennett, C.H. (1992), ‘Quantum cryptography using any two nonorthogonal states’, Physical Review Letters 68(21), 3121–3124.
Bennett, C.H. (1995), ‘Quantum information and computation’, Physics Today 48(10), 24–30.
Bennett, C.H. (2004), ‘A resource-based view of quantum information’, Quantum Information and Computation 4, 460–466.
Bennett, C.H., Bernstein, H. J, Popescu, S & Schumacher, B (1996), ‘Concentrating partial entanglement by local operations’, Physical Review A 53(4), 2046–2052. arXiv:quant-ph/9511030.
Bennett, C.H. & Brassard, G (1984), ‘Quantum cryptography: Public key distribution and coin tossing’, in Proceedings of IEEE International Conference on Computers Systems and Signal Processing, Bangalore, India, pp. 175–179.
Bennett, C.H., Brassard, G, Crépeau, C, Jozsa, R, Peres, A & Wootters, W. K (1993), ‘Teleporting an unknown quantum state via dual classical and Einstein– Podolsky–Rosen channels’, Physical Review Letters 70(13), 1895–1899.
Bennett, C.H., Brassard, G & Ekert, A. K (1992), ‘Quantum cryptography’, Scientific American, 50–57.
Bennett, C.H., Brassard, G & Mermin, N. D (1992), ‘Quantum cryptography without Bell's theorem’, Physical Review Letters 68(5), 557–559.
Bennett, C.H., Brassard, G, Popescu, S, Schumacher, B, Smolin, J. A & Wootters, W. K (1996), ‘Purification of noisy entanglement and faithful teleportation via noisy channels’, Physical Review Letters 76(5), 722–725. arXiv:quant-ph/9511027.
Bennett, C.H., Devetak, I, Harrow, A. W, Shor, P. W & Winter, A (2014), ‘The quantum reverse Shannon theorem and resource tradeoffs for simulating quantum channels’, IEEE Transactions on Information Theory 60(5), 2926–2959. arXiv:0912.5537.
Bennett, C.H., DiVincenzo, D. P., Shor, P.W., Smolin, J. A,Terhal, B. M & Wootters, W. K (2001), ‘Remote state preparation’, Physical Review Letters 87(7), 077902.
Bennett, C.H., DiVincenzo, D. P & Smolin, J. A (1997), ‘Capacities of quantum erasure channels’, Physical Review Letters 78(16), 3217–3220. arXiv:quant-ph/9701015.
Bennett, C.H., DiVincenzo, D. P, Smolin, J. A & Wootters, W. K. (1996), ‘Mixed-state entanglement and quantum error correction’, Physical Review A 54(5), 3824–3851. arXiv:quant-ph/9604024.
Bennett, C.H., Harrow, A. W & Lloyd, S (2006), ‘Universal quantum data compression via nondestructive tomography’, Physical Review A 73(3), 032336. arXiv:quant-ph/0403078.
Bennett, C.H., Hayden, P, Leung, D. W, Shor, P. W & Winter, A (2005), ‘Remote preparation of quantum states’, IEEE Transactions on Information Theory 51(1), 56–74. arXiv:quant-ph/0307100.
Bennett, C.H., Shor, P. W, Smolin, J. A & Thapliyal, A. V (1999), ‘Entanglementassisted classical capacity of noisy quantum channels’, Physical Review Letters 83(15), 3081–3084. arXiv:quant-ph/9904023.
Bennett, C.H., Shor, P. W, Smolin, J. A & Thapliyal, A. V (2002), ‘Entanglementassisted capacity of a quantum channel and the reverse Shannon theorem’, IEEETransactions on Information Theory 48(10), 2637–2655. arXiv:quant-ph/0106052.
Bennett, C.H. & Wiesner, S. J (1992), ‘Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states’, Physical Review Letters 69(20), 2881–2884.
Berger, T (1971), Rate Distortion Theory: A Mathematical Basis for Data Compression, Prentice-Hall, Englewood Cliffs, NJ.
Berger, T (1977), ‘Multiterminal source coding’, The Information Theory Approach to Communications, Springer-Verlag, New York, NY.
Bergh, J & Lofstrom, J. (1976), Interpolation Spaces, Springer-Verlag, Heidelberg.
Berta, M., Brandao, F.G. S. L., Christandl, M. & Wehner, S (2013), ‘Entanglement cost of quantum channels’, IEEE Transactions on Information Theory 59(10), 6779–6795. arXiv:1108.5357.
Berta, M., Christandl, M, Colbeck, R, Renes, J. M & Renner, R (2010), ‘The uncertainty principle in the presence of quantum memory’, Nature Physics 6, 659–662. arXiv:0909.0950.
Berta, M., Christandl, M & Renner, R (2011), ‘The quantum reverse Shannon theorem based on one-shot information theory’, Communications in Mathematical Physics 306(3), 579–615. arXiv:0912.3805.
Berta, M., Lemm, M & Wilde, M. M (2015), ‘Monotonicity of quantum relative entropy and recoverability’, Quantum Information and Computation 15(15&16), 1333–1354. arXiv:1412.4067.
Berta, M., Renes, J. M & Wilde, M. M (2014), ‘Identifying the information gain of a quantum measurement’, IEEE Transactions on Information Theory 60(12), 7987–8006. arXiv:1301.1594.
Berta, M., Seshadreesan, K & Wilde, M. M (2015), ‘Rényi generalizations of the conditional quantum mutual information’, Journal of Mathematical Physics 56(2), 022205. arXiv:1403.6102.
Berta, M & Tomamichel, M (2016), ‘The fidelity of recovery is multiplicative’, IEEETransactions on Information Theory 62(4), 1758–1763. arXiv:1502.07973.
Bhatia, R (1997), Matrix Analysis, Springer-Verlag, Heidelberg.
Blume-Kohout, R., Croke, S & Gottesman, D (2014), ‘Streaming universal distortionfree entanglement concentration’, IEEE Transactions on Information Theory 60(1), 334–350. arXiv:0910.5952.
Boche, H & Notzel, J (2014), ‘The classical–quantum multiple access channel with conferencing encoders and with common messages’, Quantum Information Processing 13(12), 2595–2617. arXiv:1310.1970.
Bohm, D (1989), Quantum Theory, Courier Dover Publications.
Bowen, G (2004), ‘Quantum feedback channels’, IEEE Transactions on Information Theory 50(10), 2429–2434. arXiv:quant-ph/0209076.
Bowen, G & Nagarajan, R (2005), ‘On feedback and the classical capacity of a noisy quantum channel’, IEEE Transactions on Information Theory 51(1), 320–324. arXiv:quant-ph/0305176.
Boyd, S & Vandenberghe, L (2004), Convex Optimization, Cambridge University Press, Cambridge, UK.
Brádler, K., Hayden, P, Touchette, D & Wilde, M. M (2010), ‘Trade-off capacities of the quantum Hadamard channels’, Physical Review A 81(6), 062312. arXiv:1001.1732.
Brandao, F.G.S. L., Christandl, M & Yard, J (2011), ‘Faithful squashed entanglement’, Communications in Mathematical Physics 306(3), 805–830. arXiv:1010.1750.
Brandao, F.G.S. L., Harrow, A. W, Oppenheim, J & Strelchuk, S (2014), ‘Quantum conditional mutual information, reconstructed states, and state redistribution’, Physical Review Letters 115(5), 050501. arXiv:1411.4921.
Brandao, F.G.S. L. & Horodecki, M (2010), ‘On Hastings’ counterexamples to the minimum output entropy additivity conjecture', Open Systems & Information Dynamics 17(1), 31–52. arXiv:0907.3210.
Braunstein, S.L., Fuchs, C. A, Gottesman, D & Lo, H.-K. (2000), ‘A quantum analog of Huffman coding’, IEEE Transactions on Information Theory 46(4), 1644–1649. arXiv:quant-ph/9805080.
Brun, T.A. (n.d.), ‘Quantum information processing course lecture slides’, http://almaak.usc.edu/∼tbrun/Course/.
Burnashev, M.V. & Holevo, A. S (1998), ‘On reliability function of quantum communication channel’, Probl. Peredachi Inform. 34(2), 1–13. arXiv:quant-ph/9703013.
Buscemi, F & Datta, N (2010), ‘The quantum capacity of channels with arbitrarily correlated noise’, IEEE Transactions on Information Theory 56(3), 1447–1460. arXiv:0902.0158.
Cai, N., Winter, A & Yeung, R. W (2004), ‘Quantum privacy and quantum wiretap channels’, Problems of Information Transmission 40(4), 318–336.
Calderbank, A.R., Rains, E. M, Shor, P. W & Sloane, N.J.A. (1997), ‘Quantum error correction and orthogonal geometry’, Physical Review Letters 78(3), 405–408. arXiv:quant-ph/9605005.
Calderbank, A.R., Rains, E. M, Shor, P. W & Sloane, N.J.A. (1998), ‘Quantum error correction via codes over GF(4)’, IEEE Transactions on Information Theory 44(4), 1369–1387. arXiv:quant-ph/9608006.
Calderbank, A.R. & Shor, P. W (1996), ‘Good quantum error-correcting codes exist’, Physical Review A 54(2), 1098–1105. arXiv:quant-ph/9512032.
Carlen, E.A. & Lieb, E. H (2014), ‘Remainder terms for some quantum entropy inequalities’, Journal of Mathematical Physics 55(4), 042201. arXiv:1402.3840.
Cerf, N.J. & Adami, C (1997), ‘Negative entropy and information in quantum mechanics’, Physical Review Letters 79(26), 5194–5197. arXiv:quant-ph/9512022.
Coles, P., Berta, M, Tomamichel, M & Wehner, S (2015), ‘Entropic uncertainty relations and their applications’. arXiv:1511.04857.
Coles, P.J., Colbeck, R, Yu, L & Zwolak, M (2012), ‘Uncertainty relations from simple entropic properties’, Physical Review Letters 108(21), 210405. arXiv:1112.0543.
Cooney, T., Mosonyi, M & Wilde, M. M (2014), ‘Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication’, Communications in Mathematical Physics 344(3), June 2016, 797–829. arXiv:1408.
Cover, T.M. & Thomas, J. A (2006), Elements of Information Theory, 2nd edn, Wiley-Interscience, New York, NY.
Csiszar, I (1967), ‘Information-type measures of difference of probability distributions and indirect observations’, Studia Sci. Math. Hungar. 2, 299–318.
Csiszár, I & Körner, J (1978), ‘Broadcast channels with confidential messages’, IEEETransactions on Information Theory 24(3), 339–348.
Csiszár, I. & Körner, J. (2011), Information Theory: Coding Theorems for Discrete Memoryless Systems, Probability and Mathematical Statistics, 2nd edn, Cambridge University Press.
Cubitt, T., Elkouss, D, Matthews, W, Ozols, M, Perez-Garcia, D. & Strelchuk, S (2015), ‘Unbounded number of channel uses may be required to detect quantum capacity’, Nature Communications 6, 6739. arXiv:1408.5115.
Czekaj, L & Horodecki, P (2009), ‘Purely quantum superadditivity of classical capacities of quantum multiple access channels’, Physical Review Letters 102(11), 110505. arXiv:0807.3977.
Dalai, M (2013), ‘Lower bounds on the probability of error for classical and classical– quantum channels’, IEEE Transactions on Information Theory 59(12), 8027–8056. arXiv:1201.5411.
Datta, N (2009), ‘Min- and max-relative entropies and a new entanglement monotone’, IEEE Transactions on Information Theory 55(6), 2816–2826. arXiv:0803.2770.
Datta, N & Hsieh, M.-H. (2010), ‘Universal coding for transmission of private information’, Journal of Mathematical Physics 51(12), 122202. arXiv:1007.2629.
Datta, N & Hsieh, M.-H. (2011), ‘The apex of the family tree of protocols: Optimal rates and resource inequalities’, New Journal of Physics 13, 093042. arXiv:1103. 1135.
Datta, N & Hsieh, M.-H. (2013), ‘One-shot entanglement-assisted quantum and classical communication’, IEEE Transactions on Information Theory 59(3), 1929–1939. arXiv:1105.3321.
Datta, N & Leditzky, F (2015), ‘Second-order asymptotics for source coding, dense coding, and pure-state entanglement conversions’, IEEE Transactions on Information Theory 61(1), 582–608. arXiv:1403.2543.
Datta, N & Renner, R (2009), ‘Smooth entropies and the quantum information spectrum’, IEEE Transactions on Information Theory 55(6), 2807–2815. arXiv:0801.0282.
Datta, N., Tomamichel, M & Wilde, M. M (2014), ‘On the Second-Order Asymptotics for Entanglement-Assisted Communication’, Quantum Information Processing (15) 6, June 2016, 2569–2591. arXiv:1405.1797.
Datta, N & Wilde, M. M (2015), ‘Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures’, Journal of Physics A 48(50), 505301. arXiv:1501.05636.
Davies, E.B. & Lewis, J. T (1970), ‘An operational approach to quantum probability’, Communications in Mathematical Physics 17(3), 239–260.
de Broglie, L (1924), ‘Recherches sur la théorie des quanta’, PhD thesis, Paris.
Deutsch, D (1985), ‘Quantum theory, the Church–Turing principle and the universal quantum computer’, Proceedings of the Royal Society of London A 400(1818), 97–117.
Devetak, I (2005), ‘The private classical capacity and quantum capacity of a quantum channel’, IEEE Transactions on Information Theory 51(1), 44–55. arXiv:quantph/0304127.
Devetak, I (2006), ‘Triangle of dualities between quantum communication protocols’, Physical Review Letters 97(14), 140503.
Devetak, I., Harrow, A. W & Winter, A (2004), ‘A family of quantum protocols’, Physical Review Letters 93(23), 239503. arXiv:quant-ph/0308044.
Devetak, I., Harrow, A. W & Winter, A (2008), ‘A resource framework for quantum Shannon theory’, IEEE Transactions on Information Theory 54(10), 4587–4618. arXiv:quant-ph/0512015.
Devetak, I., Junge, M, King, C & Ruskai, M. B (2006), ‘Multiplicativity of completely bounded p-norms implies a new additivity result’, Communications in Mathematical Physics 266(1), 37–63. arXiv:quant-ph/0506196.
Devetak, I & Shor, P. W (2005), ‘The capacity of a quantum channel for simultaneous transmission of classical and quantum information’, Communications in Mathematical Physics 256(2), 287–303. arXiv:quant-ph/0311131.
Devetak, I & Winter, A (2003), ‘Classical data compression with quantum side information’, Physical Review A 68(4), 042301. arXiv:quant-ph/0209029.
Devetak, I & Winter, A (2004), ‘Relating quantum privacy and quantum coherence: An operational approach’, Physical Review Letters 93(8), 080501. arXiv:quantph/ 0307053.
Devetak, I & Winter, A (2005), ‘Distillation of secret key and entanglement from quantum states’, Proceedings of the Royal Society A 461(2053), 207–235. arXiv:quant-ph/0306078.
Devetak, I & Yard, J (2008), ‘Exact cost of redistributing multipartite quantum states’, Physical Review Letters 100(23), 230501.
Dieks, D (1982), ‘Communication by EPR devices’, Physics Letters A 92, 271.
Ding, D & Wilde, M. M (2015), ‘Strong converse exponents for the feedback-assisted classical capacity of entanglement-breaking channels’. arXiv:1506.02228.
Dirac, P.A.M. (1982), The Principles of Quantum Mechanics (International Series of Monographs on Physics), Oxford University Press, USA.
DiVincenzo, D.P., Horodecki, M, Leung, D. W, Smolin, J. A & Terhal, B. M (2004), ‘Locking classical correlations in quantum states’, Physical Review Letters 92(6), 067902. arXiv:quant-ph/0303088.
DiVincenzo, D.P., Shor, P. W & Smolin, J. A (1998), ‘Quantum-channel capacity of very noisy channels’, Physical Review A 57(2), 830–839. arXiv:quant-ph/9706061.
Dowling, J.P. & Milburn, G. J (2003), ‘Quantum technology: The second quantum revolution’, Philosophical Transactions of The Royal Society of London Series A 361(1809), 1655–1674. arXiv:quant-ph/0206091.
Dupuis, F (2010), ‘The decoupling approach to quantum information theory’, PhD thesis, University of Montreal. arXiv:1004.1641.
Dupuis, F., Berta, M, Wullschleger, J & Renner, R (2014), ‘One-shot decoupling’, Communications in Mathematical Physics 328(1), 251–284. arXiv:1012.6044.
Dupuis, F., Florjanczyk, J, Hayden, P & Leung, D (2013), ‘The locking-decoding frontier for generic dynamics’, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 469(2159). arXiv:1011.1612.
Dupuis, F., Hayden, P & Li, K (2010), ‘A father protocol for quantum broadcast channels’, IEEE Transactions on Information Theory 56(6), 2946–2956. arXiv:quantph/ 0612155.
Dupuis, F & Wilde, M. M (2016), ‘Swiveled Rényi entropies’, Quantum Information Processing 15(3), 1309–1345. arXiv:1506.00981.
Dutil, N (2011), ‘Multiparty quantum protocols for assisted entanglement distillation’, PhD thesis, McGill University. arXiv:1105.4657.
Einstein, A (1905), ‘Über einen die erzeugung und verwandlung des lichtes betreffenden heuristischen gesichtspunkt’, Annalen der Physik 17, 132–148.
Einstein, A., Podolsky, B & Rosen, N (1935), ‘Can quantum-mechanical description of physical reality be considered complete?’, Physical Review 47, 777–780.
Ekert, A.K. (1991), ‘Quantum cryptography based on Bell's theorem’, Physical Review Letters 67(6), 661–663.
Elias, P (1972), ‘The efficient construction of an unbiased random sequence’, Annals of Mathematical Statistics 43(3), 865–870.
Elkouss, D & Strelchuk, S (2015), ‘Superadditivity of private information for any number of uses of the channel’, Physical Review Letters 115(4), 040501. arXiv:1502.05326.
Fannes, M (1973), ‘A continuity property of the entropy density for spin lattices’, Communications in Mathematical Physics 31, 291.
Fano, R.M. (2008), ‘Fano inequality’, Scholarpedia 3(10), 6648.
Fawzi, O., Hayden, P, Savov, I, Sen, P & Wilde, M. M (2012), ‘Classical communication over a quantum interference channel’, IEEE Transactions on Information Theory 58(6), 3670–3691. arXiv:1102.2624.
Fawzi, O., Hayden, P & Sen, P (2013), ‘From low-distortion norm embeddings to explicit uncertainty relations and efficient information locking’, Journal of the ACM 60(6), 44:1–44:61. arXiv:1010.3007.
Fawzi, O & Renner, R (2015), ‘Quantum conditional mutual information and approximate Markov chains’, Communications in Mathematical Physics 340(2), 575–611. arXiv:1410.0664.
Feller, W (1971), An Introduction to Probability Theory and Its Applications, 2nd edn, John Wiley and Sons.
Feynman, R.P. (1982), ‘Simulating physics with computers’, International Journal of Theoretical Physics 21, 467–488.
Feynman, R.P. (1998), Feynman Lectures On Physics (3 Volume Set), Addison Wesley Longman.
Fuchs, C (1996), ‘Distinguishability and Accessible Information in Quantum Theory’, PhD thesis, University of New Mexico. arXiv:quant-ph/9601020.
Fuchs, C.A. & Caves, C. M (1995), ‘Mathematical techniques for quantum communication theory’, Open Systems & Information Dynamics 3(3), 345–356. arXiv:quantph/ 9604001.
Fuchs, C.A. & van de Graaf, J. (1998), ‘Cryptographic distinguishability measures for quantum mechanical states’, IEEE Transactions on Information Theory 45(4), 1216–1227. arXiv:quant-ph/9712042.
Fukuda, M & King, C (2010), ‘Entanglement of random subspaces via the Hastings bound’, Journal of Mathematical Physics 51(4), 042201. arXiv:0907.5446.
Fukuda, M., King, C & Moser, D. K (2010), ‘Comments on Hastings’ additivity counterexamples', Communications in Mathematical Physics 296(1), 111–143. arXiv:0905.3697.
Gamal, A.E. & Kim, Y.-H. (2012), Network Information Theory, Cambridge University Press. arXiv:1001.3404.
García-Patrón, R., Pirandola, S, Lloyd, S & Shapiro, J. H (2009), ‘Reverse coherent information’, Physical Review Letters 102(21), 210501. arXiv:0808.0210.
Gerlach, W & Stern, O (1922), ‘Das magnetische moment des silberatoms’, Zeitschrift für Physik 9, 353–355.
Giovannetti, V & Fazio, R (2005), ‘Information-capacity description of spin-chain correlations’, Physical Review A 71(3), 032314. arXiv:quant-ph/0405110.
Giovannetti, V., Guha, S, Lloyd, S, Maccone, L & Shapiro, J. H (2004), ‘Minimum output entropy of bosonic channels: A conjecture’, Physical Review A 70(3), 032315. arXiv:quant-ph/0404005.
Giovannetti, V., Guha, S, Lloyd, S, Maccone, L, Shapiro, J. H & Yuen, H. P (2004), ‘Classical capacity of the lossy bosonic channel: The exact solution’, Physical Review Letters 92(2), 027902. arXiv:quant-ph/0308012.
Giovannetti, V., Holevo, A. S & García-Patrón, R (2015), ‘A solution of Gaussian optimizer conjecture for quantum channels’, Communications in Mathematical Physics 334(3), 1553–1571.
Giovannetti, V., Holevo, A. S, Lloyd, S & Maccone, L (2010), ‘Generalized minimal output entropy conjecture for one-mode Gaussian channels: definitions and some exact results’, Journal of Physics A: Mathematical and Theoretical 43(41), 415305. arXiv:1004.4787.
Giovannetti, V., Lloyd, S & Maccone, L (2012), ‘Achieving the Holevo bound via sequential measurements’, Physical Review A 85, 012302. arXiv:1012.0386.
Giovannetti, V., Lloyd, S, Maccone, L & Shor, P. W (2003a), ‘Broadband channel capacities’, Physical Review A 68(6), 062323. arXiv:quant-ph/0307098.
Giovannetti, V., Lloyd, S, Maccone, L & Shor, P. W (2003b), ‘Entanglement assisted capacity of the broadband lossy channel’, Physical Review Letters 91(4), 047901. arXiv:quant-ph/0304020.
Glauber, R.J. (1963a), ‘Coherent and incoherent states of the radiation field’, Physical Review 131(6), 2766–2788.
Glauber, R.J. (1963b), ‘The quantum theory of optical coherence’, Physical Review 130(6), 2529–2539.
Glauber, R.J. (2005), ‘One hundred years of light quanta’, in K, Grandin, ed., Les Prix Nobel. The Nobel Prizes 2005, Nobel Foundation, pp. 90–91.
Gordon, J.P. (1964), ‘Noise at optical frequencies; information theory’, in P.A, Miles, ed., Quantum Electronics and Coherent Light; Proceedings of the International School of Physics Enrico Fermi, Course XXXI, Academic Press New York, pp. 156–181.
Gottesman, D (1996), ‘Class of quantum error-correcting codes saturating the quantum Hamming bound’, Physical Review A 54(3), 1862–1868. arXiv:quant-ph/9604038.
Gottesman, D (1997), ‘Stabilizer Codes and Quantum Error Correction’, PhD thesis, California Institute of Technology. arXiv:quant-ph/9705052.
Grafakos, L (2008), Classical Fourier Analysis, 2nd edn, Springer.
Grassl, M., Beth, T & Pellizzari, T (1997), ‘Codes for the quantum erasure channel’, Physical Review A 56(1), 33–38. arXiv:quant-ph/9610042.
Greene, B (1999), The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, W. W. Norton & Company.
Griffiths, D.J. (1995), Introduction to Quantum Mechanics, Prentice-Hall, Inc.
Groisman, B., Popescu, S & Winter, A (2005), ‘Quantum, classical, and total amount of correlations in a quantum state’, Physical Review A 72(3), 032317. arXiv:quantph/ 0410091.
Grudka, A & Horodecki, P (2010), ‘Nonadditivity of quantum and classical capacities for entanglement breaking multiple-access channels and the butterfly network’, Physical Review A 81(6), 060305. arXiv:0906.1305.
Guha, S (2008), ‘Multiple-User Quantum Information Theory for Optical Communication Channels’, PhD thesis, Massachusetts Institute of Technology.
Guha, S., Hayden, P, Krovi, H, Lloyd, S, Lupo, C, Shapiro, J. H, Takeoka, M & Wilde, M. M (2014), ‘Quantum enigma machines and the locking capacity of a quantum channel’, Physical Review X 4(1), 011016. arXiv:1307.5368.
Guha, S & Shapiro, J. H (2007), ‘Classical information capacity of the bosonic broadcast channel’, in Proceedings of the IEEE International Symposium on Information Theory, Nice, France, pp. 1896–1900. arXiv:0704.1901.
Guha, S., Shapiro, J. H & Erkmen, B. I (2007), ‘Classical capacity of bosonic broadcast communication and a minimum output entropy conjecture’, Physical Review A 76(3), 032303. arXiv:0706.3416.
Guha, S., Shapiro, J. H & Erkmen, B. I (2008), ‘Capacity of the bosonic wiretap channel and the entropy photon-number inequality’, in Proceedings of the IEEE International Symposium on Information Theory, Toronto, Ontario, Canada, pp. 91–95. arXiv:0801.0841.
Gupta, M & Wilde, M. M (2015), ‘Multiplicativity of completely bounded p-norms implies a strong converse for entanglement-assisted capacity’, Communications in Mathematical Physics 334(2), 867–887. arXiv:1310.7028.
Hamada, M (2005), ‘Information rates achievable with algebraic codes on quantum discrete memoryless channels’, IEEE Transactions on Information Theory 51(12), 4263–4277. arXiv:quant-ph/0207113.
Harrington, J & Preskill, J (2001), ‘Achievable rates for the Gaussian quantum channel’, Physical Review A 64(6), 062301. arXiv:quant-ph/0105058.
Harrow, A (2004), ‘Coherent communication of classical messages’, Physical Review Letters 92(9), 097902. arXiv:quant-ph/0307091.
Harrow, A.W. & Lo, H-K. (2004), ‘A tight lower bound on the classical communication cost of entanglement dilution’, IEEE Transactions on Information Theory 50(2), 319–327. arXiv:quant-ph/0204096.
Hastings, M.B. (2009), ‘Superadditivity of communication capacity using entangled inputs’, Nature Physics 5, 255–257. arXiv:0809.3972.
Hausladen, P., Jozsa, R, Schumacher, B, Westmoreland, M & Wootters, W. K (1996), ‘Classical information capacity of a quantum channel’, Physical Review A 54(3), 1869–1876.
Hausladen, P., Schumacher, B, Westmoreland, M & Wootters, W. K (1995), ‘Sending classical bits via quantum its’, Annals of the New York Academy of Sciences 755, 698–705.
Hayashi, M (2002), ‘Exponents of quantum fixed-length pure-state source coding’, Physical Review A 66(3), 032321. arXiv:quant-ph/0202002.
Hayashi, M (2006), Quantum Information: An Introduction, Springer.
Hayashi, M (2007), ‘Error exponent in asymmetric quantum hypothesis testing and its application to classical–quantum channel coding’, Physical Review A 76(6), 062301. arXiv:quant-ph/0611013.
Hayashi, M., Koashi, M, Matsumoto, K, Morikoshi, F & Winter, A (2003), ‘Error exponents for entanglement concentration’, Journal of Physics A: Mathematical and General 36(2), 527. arXiv:quant-ph/0206097.
Hayashi, M & Matsumoto, K (2001), ‘Variable length universal entanglement concentration by local operations and its application to teleportation and dense coding’. arXiv:quant-ph/0109028.
Hayashi, M & Nagaoka, H (2003), ‘General formulas for capacity of classical–quantum channels’, IEEE Transactions on Information Theory 49(7), 1753–1768. arXiv:quantph/ 0206186.
Hayden, P (2007), ‘The maximal p-norm multiplicativity conjecture is false’. arXiv:0707.3291.
Hayden, P., Horodecki, M, Winter, A & Yard, J (2008), ‘A decoupling approach to the quantum capacity’, Open Systems & Information Dynamics 15(1), 7–19. arXiv:quant-ph/0702005.
Hayden, P., Jozsa, R, Petz, D & Winter, A (2004), ‘Structure of states which satisfy strong subadditivity of quantum entropy with equality’, Communications in Mathematical Physics 246(2), 359–374. arXiv:quant-ph/0304007.
Hayden, P., Jozsa, R & Winter, A (2002), ‘Trading quantum for classical resources in quantum data compression’, Journal of Mathematical Physics 43(9), 4404–4444. arXiv:quant-ph/0204038.
Hayden, P., Leung, D, Shor, P. W & Winter, A (2004), ‘Randomizing quantum states: Constructions and applications’, Communications in Mathematical Physics 250(2), 371–391. arXiv:quant-ph/0307104.
Hayden, P., Shor, P. W & Winter, A (2008), ‘Random quantum codes from Gaussian ensembles and an uncertainty relation’, Open Systems & Information Dynamics 15(1), 71–89. arXiv:0712.0975.
Hayden, P & Winter, A (2003), ‘Communication cost of entanglement transformations’, Physical Review A 67(1), 012326. arXiv:quant-ph/0204092.
Hayden, P & Winter, A (2008), ‘Counterexamples to the maximal p-norm multiplicativity conjecture for all’, Communications in Mathematical Physics 284(1), 263–280. arXiv:0807.4753.
Heinosaari, T & Ziman, M (2012), The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement, Cambridge University Press.
Heisenberg, W (1925), ‘ Über quantentheoretische umdeutung kinematischer und mechanischer beziehungen’, Zeitschrift für Physik 33, 879–893.
Helstrom, C.W. (1969), ‘Quantum detection and estimation theory’, Journal of Statistical Physics 1, 231–252.
Helstrom, C.W. (1976), Quantum Detection and Estimation Theory, Academic, New York, NY.
Herbert, N (1982), ‘Flash—a superluminal communicator based upon a new kind of quantum measurement’, Foundations of Physics 12(12), 1171–1179.
Hirche, C & Morgan, C (2015), ‘An improved rate region for the classical–quantum broadcast channel’, Proceedings of the 2015 IEEE International Symposium on Information Theory pp. 2782–2786. arXiv:1501.07417.
Hirche, C., Morgan, C & Wilde, M. M (2016), ‘Polar codes in network quantum information theory’, IEEE Transactions on Information Theory 62(2), 915–924. arXiv:1409.7246.
Hirschman, I.I. (1952), ‘A convexity theorem for certain groups of transformations’, Journal d'Analyse Mathématique 2(2), 209–218.
Holevo, A.S. (1973a), ‘Bounds for the quantity of information transmitted by a quantum communication channel’, Problems of Information Transmission 9, 177–183.
Holevo, A.S. (1973b), ‘Statistical problems in quantum physics’, in Second Japan- USSR Symposium on Probability Theory, Vol. 330 of Lecture Notes in Mathematics, Springer Berlin/Heidelberg, pp. 104–119.
Holevo, A.S. (1998), ‘The capacity of the quantum channel with general signal states’, IEEE Transactions on Information Theory 44(1), 269–273. arXiv:quant-ph/9611023.
Holevo, A.S. (2000), ‘Reliability function of general classical–quantum channel’, IEEETransactions on Information Theory 46(6), 2256–2261. arXiv:quant-ph/9907087.
Holevo, A.S. (2002a), An Introduction to Quantum Information Theory, Moscow Center of Continuous Mathematical Education, Moscow. In Russian.
Holevo, A.S. (2002b), ‘On entanglement assisted classical capacity’, Journal of Mathematical Physics 43(9), 4326–4333. arXiv:quant-ph/0106075.
Holevo, A.S. (2012), Quantum Systems, Channels, Information, de Gruyter Studies in Mathematical Physics (Book 16), de Gruyter.
Holevo, A.S. & Werner, R. F (2001), ‘Evaluating capacities of bosonic Gaussian channels’, Physical Review A 63(3), 032312. arXiv:quant-ph/9912067.
Horodecki, M (1998), ‘Limits for compression of quantum information carried by ensembles of mixed states’, Physical Review A 57(5), 3364–3369. arXiv:quantph/9712035.
Horodecki, M., Horodecki, P & Horodecki, R (1996), ‘Separability of mixed states: necessary and sufficient conditions’, Physics Letters A 223(1-2), 1–8. arXiv:quantph/ 9605038.
Horodecki, M., Horodecki, P, Horodecki, R, Leung, D & Terhal, B (2001), ‘Classical capacity of a noiseless quantum channel assisted by noisy entanglement’, Quantum Information and Computation 1(3), 70–78. arXiv:quant-ph/0106080.
Horodecki, M., Oppenheim, J & Winter, A (2005), ‘Partial quantum information’, Nature 436, 673–676.
Horodecki, M., Oppenheim, J & Winter, A (2007), ‘Quantum state merging and negative information’, Communications in Mathematical Physics 269(1), 107–136. arXiv:quant-ph/0512247.
Horodecki, M., Shor, P. W & Ruskai, M. B (2003), ‘Entanglement breaking channels’, Reviews in Mathematical Physics 15(6), 629–641. arXiv:quant-ph/0302031.
Horodecki, P (1997), ‘Separability criterion and inseparable mixed states with positive partial transposition’, Physics Letters A 232(5), 333–339. arXiv:quant-ph/9703004.
Horodecki, R & Horodecki, P (1994), ‘Quantum redundancies and local realism’, Physics Letters A 194(3), 147–152.
Horodecki, R., Horodecki, P, Horodecki, M & Horodecki, K (2009), ‘Quantum entanglement’, Reviews of Modern Physics 81(2), 865–942. arXiv:quant-ph/0702225.
Hsieh, M-H., Devetak, I & Winter, A (2008), ‘Entanglement-assisted capacity of quantum multiple-access channels’, IEEE Transactions on Information Theory 54(7), 3078–3090. arXiv:quant-ph/0511228.
Hsieh, M-H, Luo, Z & Brun, T (2008), ‘Secret-key-assisted private classical communication capacity over quantum channels’, Physical Review A 78(4), 042306. arXiv:0806.3525.
Hsieh, M-H & Wilde, M. M (2009), ‘Public and private communication with a quantum channel and a secret key’, Physical Review A 80(2), 022306. arXiv:0903. 3920.
Hsieh, M-H & Wilde, M. M (2010a), ‘Entanglement-assisted communication of classical and quantum information’, IEEE Transactions on Information Theory 56(9), 4682–4704. arXiv:0811.4227.
Hsieh, M-H & Wilde, M. M (2010b), ‘Trading classical communication, quantum communication, and entanglement in quantum Shannon theory’, IEEE Transactions on Information Theory 56(9), 4705–4730. arXiv:0901.3038.
Jaynes, E.T. (1957a), ‘Information theory and statistical mechanics’, Physical Review 106, 620.
Jaynes, E.T. (1957b), ‘Information theory and statistical mechanics II’, Physical Review 108, 171.
Jaynes, E.T. (2003), Probability Theory: The Logic of Science, Cambridge University Press.
Jencova, A (2012), ‘Reversibility conditions for quantum operations’, Reviews in Mathematical Physics 24(7), 1250016. arXiv:1107.0453.
Jochym-O'Connor, T., Brádler, K. & Wilde, M. M (2011), ‘Trade-off coding for universal qudit cloners motivated by the Unruh effect’, Journal of Physics A: Mathematical and Theoretical 44(41), 415306. arXiv:1103.0286.
Jozsa, R (1994), ‘Fidelity for mixed quantum states’, Journal of Modern Optics 41(12), 2315–2323.
Jozsa, R., Horodecki, M, Horodecki, P & Horodecki, R (1998), ‘Universal quantum information compression’, Physical Review Letters 81(8), 1714–1717. arXiv:quantph/ 9805017.
Jozsa, R & Presnell, S (2003), ‘Universal quantum information compression and degrees of prior knowledge’, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 459(2040), 3061–3077. arXiv:quant-ph /0210196.
Jozsa, R & Schumacher, B (1994), ‘A new proof of the quantum noiseless coding theorem’, Journal of Modern Optics 41(12), 2343–2349.
Junge, M., Renner, R, Sutter, D, Wilde, M. M & Winter, A (2015), ‘Universal recovery from a decrease of quantum relative entropy’. arXiv:1509.07127.
Kaye, P & Mosca, M (2001), ‘Quantum networks for concentrating entanglement’, Journal of Physics A: Mathematical and General 34(35), 6939. arXiv:quantph/ 0101009.
Kelvin, W.T. (1901), ‘Nineteenth-century clouds over the dynamical theory of heat and light’, The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 2(6), 1.
Kemperman, J.H.B. (1969), ‘On the optimum rate of transmitting information’, Lecture Notes in Mathematics 89, 126–169. In Probability and Information Theory.
Kim, I.H. (2013), ‘Application of conditional independence to gapped quantum manybody systems’, www.physics.usyd.edu.au/quantum/Coogee2013. Slide 43.
King, C (2002), ‘Additivity for unital qubit channels’, Journal of Mathematical Physics 43(10), 4641–4653. arXiv:quant-ph/0103156.
King, C (2003), ‘The capacity of the quantum depolarizing channel’, IEEE Transactions on Information Theory 49(1), 221–229. arXiv:quant-ph/0204172.
King, C., Matsumoto, K, Nathanson, M & Ruskai, M. B (2007), ‘Properties of conjugate channels with applications to additivity and multiplicativity’, Markov Processes and Related Fields 13(2), 391–423. J.T Lewis memorial issue. arXiv:quantph/ 0509126.
Kitaev, A.Y. (1997), Uspekhi Mat. Nauk. 52(53).
Klesse, R (2008), ‘A random coding based proof for the quantum coding theorem’, Open Systems & Information Dynamics 15(1), 21–45. arXiv:0712.2558.
Knill, E.H., Laflamme, R & Zurek, W. H (1998), ‘Resilient quantum computation’, Science 279, 342–345. quant-ph/9610011.
Koashi, M & Imoto, N (2001), ‘Teleportation cost and hybrid compression of quantum signals’. arXiv:quant-ph/0104001.
Koenig, R., Renner, R & Schaffner, C (2009), ‘The operational meaning of minand max-entropy’, IEEE Transactions on Information Theory 55(9), 4337–4347. arXiv:0807.1338.
Koenig, R & Wehner, S (2009), ‘A strong converse for classical channel coding using entangled inputs’, Physical Review Letters 103(7), 070504. arXiv:0903.2838.
König, R., Renner, R, Bariska, A & Maurer, U (2007), ‘Small accessible quantum information does not imply security’, Physical Review Letters 98(14), 140502. arXiv:quant-ph/0512021.
Kremsky, I., Hsieh, M-H. & Brun, T. A (2008), ‘Classical enhancement of quantumerror- correcting codes’, Physical Review A 78(1), 012341. arXiv:0802.2414.
Kullback, S (1967), ‘A lower bound for discrimination in terms of variation’, IEEE-IT 13, 126–127.
Kumagai, W & Hayashi, M (2013), ‘Entanglement concentration is irreversible’, Physical Review Letters 111(13), 130407. arXiv:1305.6250.
Kuperberg, G (2003), ‘The capacity of hybrid quantum memory’, IEEE Transactions on Information Theory 49(6), 1465–1473. arXiv:quant-ph/0203105.
Laflamme, R., Miquel, C, Paz, J. P & Zurek, W. H (1996), ‘Perfect quantum error correcting code’, Physical Review Letters 77(1), 198–201.
Landauer, R (1995), ‘Is quantum mechanics useful?’, Philosophical Transactions of the Royal Society: Physical and Engineering Sciences 353(1703), 367–376.
Lanford, O.E. & Robinson, D. W (1968), ‘Mean entropy of states in quantumstatistical mechanics’, Journal of Mathematical Physics 9(7), 1120–1125.
Levitin, L.B. (1969), ‘On the quantum measure of information’, in Proceedings of the Fourth All-Union Conference on Information and Coding Theory, Sec. II, Tashkent.
Li, K & Winter, A (2014), ‘Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps’. arXiv:1410.4184.
Li, K., Winter, A, Zou, X & Guo, G-C. (2009), ‘Private capacity of quantum channels is not additive’, Physical Review Letters 103(12), 120501. arXiv:0903.4308.
Lieb, E.H. (1973), ‘Convex trace functions and the Wigner–Yanase–Dyson conjecture’, Advances in Mathematics 11, 267–288.
Lieb, E.H. & Ruskai, M. B (1973a), ‘A fundamental property of quantum-mechanical entropy’, Physical Review Letters 30(10), 434–436.
Lieb, E.H. & Ruskai, M. B (1973b), ‘Proof of the strong subadditivity of quantummechanical entropy’, Journal of Mathematical Physics 14, 1938–1941.
Lindblad, G (1975), ‘Completely positive maps and entropy inequalities’, Communications in Mathematical Physics 40(2), 147–151.
Lloyd, S (1997), ‘Capacity of the noisy quantum channel’, Physical Review A 55(3), 1613–1622. arXiv:quant-ph/9604015.
Lloyd, S., Giovannetti, V & Maccone, L (2011), ‘Sequential projective measurements for channel decoding’, Physical Review Letters 106(25), 250501. arXiv:1012.0106.
Lo, H-K. (1995), ‘Quantum coding theorem for mixed states’, Optics Communications 119(5-6), 552–556. arXiv:quant-ph/9504004.
Lo, H-K. & Popescu, S (1999), ‘Classical communication cost of entanglement manipulation: Is entanglement an interconvertible resource?’, Physical Review Letters 83(7), 1459–1462.
Lo, H-K. & Popescu, S (2001), ‘Concentrating entanglement by local actions: Beyond mean values’, Physical Review A 63(2), 022301. arXiv:quant-ph/9707038.
Lupo, C & Lloyd, S (2014), ‘Quantum-locked key distribution at nearly the classical capacity rate’, Physical Review Letters 113(16), 160502. arXiv:1406.4418.
Lupo, C & Lloyd, S (2015), ‘Quantum data locking for high-rate private communication’, New Journal of Physics 17(3), 033022.
MacKay, D (2003), Information Theory, Inference, and Learning Algorithms, Cambridge University Press.
Matthews, W & Wehner, S (2014), ‘Finite blocklength converse bounds for quantum channels’, IEEE Transactions on Information Theory 60(11), 7317–7329. arXiv:1210.4722.
McEvoy, J.P. & Zarate, O (2004), Introducing Quantum Theory, 3rd edn, Totem Books.
Misner, C.W., Thorne, K. S & Zurek, W. H (2009), ‘John Wheeler, relativity, and quantum information’, Physics Today.
Morgan, C & Winter, A (2014), ‘“Pretty strong” converse for the quantum capacity of degradable channels’, IEEE Transactions on Information Theory 60(1), 317–333. arXiv:1301.4927.
Mosonyi, M (2005), ‘Entropy, Information and Structure of Composite Quantum States’, PhD thesis, Katholieke Universiteit Leuven. Available at https://lirias.kuleuven.be/bitstream/1979/41/2/thesisbook9.pdf.
Mosonyi, M & Datta, N (2009), ‘Generalized relative entropies and the capacity of classical–quantum channels’, Journal of Mathematical Physics 50(7), 072104. arXiv:0810.3478.
Mosonyi, M & Petz, D (2004), ‘Structure of sufficient quantum coarse-grainings’, Letters in Mathematical Physics 68(1), 19–30. arXiv:quant-ph/0312221.
Mullins, J (2001), ‘The topsy turvy world of quantum computing’, IEEE Spectrum 38(2), 42–49.
Nielsen, M.A. (1998), ‘Quantum information theory’, PhD thesis, University of New Mexico. arXiv:quant-ph/0011036.
Nielsen, M.A. (1999), ‘Conditions for a class of entanglement transformations’, Physical Review Letters 83(2), 436–439. arXiv:quant-ph/9811053.
Nielsen, M.A. (2002), ‘A simple formula for the average gate fidelity of a quantum dynamical operation’, Physics Letters A 303(4), 249–252.
Nielsen, M.A. & Chuang, I. L (2000), Quantum Computation and Quantum Information, Cambridge University Press.
Ogawa, T & Nagaoka, H (1999), ‘Strong converse to the quantum channel coding theorem’, IEEE Transactions on Information Theory 45(7), 2486–2489. arXiv:quantph/9808063.
Ogawa, T & Nagaoka, H (2007), ‘Making good codes for classical–quantum channel coding via quantum hypothesis testing’, IEEE Transactions on Information Theory 53(6), 2261–2266.
Ohya, M & Petz, D (1993), Quantum Entropy and Its Use, Springer.
Ollivier, H & Zurek, W. H (2001), ‘Quantum discord: A measure of the quantumness of correlations’, Physical Review Letters 88(1), 017901. arXiv:quant-ph/0105072.
Ozawa, M (1984), ‘Quantum measuring processes of continuous observables’, Journal of Mathematical Physics 25(1), 79–87.
Ozawa, M (2000), ‘Entanglement measures and the Hilbert–Schmidt distance’, Physics Letters A 268(3), 158–160. arXiv:quant-ph/0002036.
Pati, A.K. & Braunstein, S. L (2000), ‘Impossibility of deleting an unknown quantum state’, Nature 404, 164–165. arXiv:quant-ph/9911090.
Peres, A (2002), ‘How the no-cloning theorem got its name’. arXiv:quant-ph/0205076.
Petz, D (1986), ‘Sufficient subalgebras and the relative entropy of states of a von Neumann algebra’, Communications in Mathematical Physics 105(1), 123–131.
Petz, D (1988), ‘Sufficiency of channels over von Neumann algebras’, Quarterly Journal of Mathematics 39(1), 97–108.
Pierce, J.R. (1973), ‘The early days of information theory’, IEEE Transactions on Information Theory IT-19(1), 3–8.
Pinsker, M.S. (1960), ‘Information and information stability of random variables and processes’, Problemy Peredaci Informacii 7. AN SSSR, Moscow. English translation: Holden-Day, San Francisco, CA, 1964.
Planck, M (1901), ‘Ueber das gesetz der energieverteilung im normalspectrum’, Annalen der Physik 4, 553–563.
Plenio, M.B., Virmani, S & Papadopoulos, P (2000), ‘Operator monotones, the reduction criterion and the relative entropy’, Journal of Physics A: Mathematical and General 33(22), L193. arXiv:quant-ph/0002075.
Preskill, J (1998), ‘Reliable quantum computers’, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 454(1969), 385–410. arXiv:quantph/9705031.
Radhakrishnan, J., Sen, P & Warsi, N (2014), ‘One-shot Marton inner bound for classical–quantum broadcast channel’. arXiv:1410.3248.
Rains, E.M. (2001), ‘A semidefinite program for distillable entanglement’, IEEE Transactions on Information Theory 47(7), 2921–2933. arXiv:quant-ph/0008047.
Reed, M & Simon, B (1975), Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness, Academic Press.
Renner, R (2005), ‘Security of Quantum Key Distribution’, PhD thesis, ETH Zurich. arXiv:quant-ph/0512258.
Rivest, R., Shamir, A & Adleman, L (1978), ‘A method for obtaining digital signatures and public-key cryptosystems’, Communications of the ACM 21(2), 120–126.
Sakurai, J.J. (1994), Modern Quantum Mechanics (2nd Edition), Addison Wesley.
Sason, I (2013), ‘Entropy bounds for discrete random variables via maximal coupling’, IEEE Transactions on Information Theory 59(11), 7118–7131. arXiv:1209.5259.
Savov, I (2008), ‘Distributed compression and squashed entanglement’, Master's thesis, McGill University. arXiv:0802.0694.
Savov, I (2012), ‘Network information theory for classical–quantum channels’, PhD thesis, McGill University, School of Computer Science. arXiv:1208.4188.
Savov, I & Wilde, M. M (2015), ‘Classical codes for quantum broadcast channels’, IEEE Transactions on Information Theory 61(12), 7017–7028. arXiv:1111.3645.
Scarani, V (2013), ‘The device-independent outlook on quantum physics (lecture notes on the power of Bell's theorem)’. arXiv:1303.3081.
Scarani, V., Bechmann-Pasquinucci, H, Cerf, N. J, Dušek, M, Lütkenhaus, N & Peev, M (2009), ‘The security of practical quantum key distribution’, Reviews of Modern Physics 81(3), 1301–1350. arXiv:0802.4155.
Scarani, V., Iblisdir, S, Gisin, N & Acín, A (2005), ‘Quantum cloning’, Reviews of Modern Physics 77(4), 1225–1256. arXiv:quant-ph/0511088.
Schrödinger, E (1926), ‘Quantisierung als eigenwertproblem’, Annalen der Physik 79, 361–376.
Schrödinger, E (1935), ‘Discussion of probability relations between separated systems’, Proceedings of the Cambridge Philosophical Society 31, 555–563.
Schumacher, B (1995), ‘Quantum coding’, Physical Review A 51(4), 2738–2747.
Schumacher, B (1996), ‘Sending entanglement through noisy quantum channels’, Physical Review A 54(4), 2614–2628.
Schumacher, B & Nielsen, M. A (1996), ‘Quantum data processing and error correction’, Physical Review A 54(4), 2629–2635. arXiv:quant-ph/9604022.
Schumacher, B & Westmoreland, M. D (1997), ‘Sending classical information via noisy quantum channels’, Physical Review A 56(1), 131–138.
Schumacher, B & Westmoreland, M. D (1998), ‘Quantum privacy and quantum coherence’, Physical Review Letters 80(25), 5695–5697. arXiv:quant-ph/9709058.
Schumacher, B & Westmoreland, M. D (2002), ‘Approximate quantum error correction’, Quantum Information Processing 1(1/2), 5–12. arXiv:quant-ph/0112106.
Sen, P (2011), ‘Achieving the Han–Kobayashi inner bound for the quantum interference channel by sequential decoding’. arXiv:1109.0802.
Seshadreesan, K.P., Berta, M & Wilde, M. M (2015), ‘Rényi squashed entanglement, discord, and relative entropy differences’, Journal of Physics A: Mathematical and Theoretical 48(39), 395303. arXiv:1410.1443.
Seshadreesan, K.P., Takeoka, M & Wilde, M. M (2015), ‘Bounds on entanglement distillation and secret key agreement for quantum broadcast channels’, IEEETransactions on Information Theory 62(5), May 2016, 2849–2866. arXiv:1503.08139.
Seshadreesan, K.P. & Wilde, M. M (2015), ‘Fidelity of recovery, squashed entanglement, and measurement recoverability’, Physical Review A 92(4), 042321. arXiv:1410.1441.
Shannon, C.E. (1948), ‘A mathematical theory of communication’, Bell System Technical Journal 27, 379–423.
Shor, P.W. (1994), ‘Algorithms for quantum computation: Discrete logarithms and factoring’, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, California, pp. 124–134.
Shor, P.W. (1995), ‘Scheme for reducing decoherence in quantum computer memory’, Physical Review A 52(4), R2493–R2496.
Shor, P.W. (1996), ‘Fault-tolerant quantum computation’, Annual IEEE Symposium on Foundations of Computer Science p. 56. arXiv:quant-ph/9605011.
Shor, P.W. (2002a), ‘Additivity of the classical capacity of entanglement-breaking quantum channels’, Journal of Mathematical Physics 43(9), 4334–4340. arXiv:quantph/ 0201149.
Shor, P.W. (2002b), ‘The quantum channel capacity and coherent information’, in Lecture Notes, MSRI Workshop on Quantum Computation.
Shor, P.W. (2004a), ‘Equivalence of additivity questions in quantum information theory’, Communications in Mathematical Physics 246(3), 453–472. arXiv:quantph/0305035.
Shor, P.W. (2004b), Quantum Information, Statistics, Probability (Dedicated to A. S. Holevo on the occasion of his 60th Birthday): The classical capacity achievable by a quantum channel assisted by limited entanglement, Rinton Press, Inc. arXiv:quantph/0402129.
Smith, G (2006), ‘Upper and Lower Bounds on Quantum Codes’, PhD thesis, California Institute of Technology.
Smith, G (2008), ‘Private classical capacity with a symmetric side channel and its application to quantum cryptography’, Physical Review A 78(2), 022306. arXiv:0705.
Smith, G., Renes, J. M & Smolin, J. A (2008), ‘Structured codes improve the Bennett–Brassard-84 quantum key rate’, Physical Review Letters 100(17), 170502. arXiv:quant-ph/0607018.
Smith, G & Smolin, J. A (2007), ‘Degenerate quantum codes for Pauli channels’, Physical Review Letters 98(3), 030501. arXiv:quant-ph/0604107.
Smith, G., Smolin, J. A & Yard, J (2011), ‘Quantum communication with Gaussian channels of zero quantum capacity’, Nature Photonics 5, 624–627. arXiv:1102.4580.
Smith, G & Yard, J (2008), ‘Quantum communication with zero-capacity channels’, Science 321(5897), 1812–1815. arXiv:0807.4935.
Steane, A.M. (1996), ‘Error correcting codes in quantum theory’, Physical Review Letters 77(5), 793–797.
Stein, E.M. (1956), ‘Interpolation of linear operators’, Transactions of the American Mathematical Society 83(2), 482–492.
Stinespring, W.F. (1955), ‘Positive functions on C*-algebras’, Proceedings of the American Mathematical Society 6, 211–216.
Sutter, D., Fawzi, O & Renner, R (2016), ‘Universal recovery map for approximate markov chains’, Proceedings of the Royal Society A 472(2186). arXiv:1504.07251.
Sutter, D., Tomamichel, M & Harrow, A. W (2015), ‘Strengthened monotonicity of relative entropy via pinched Petz recovery map’, IEEE Transactions on Information Theory 62(5), 2016, 2907–2913. arXiv:1507.00303.
Tomamichel, M (2012), ‘A Framework for Non-Asymptotic Quantum Information Theory’, PhD thesis, ETH Zurich. arXiv:1203.2142.
Tomamichel, M (2016), Quantum Information Processing with Finite Resources — Mathematical Foundations, Vol. 5 of SpringerBriefs in Mathematical Physics, Springer. arXiv:1504.00233.
Tomamichel, M., Berta, M & Renes, J. M (2015), ‘Quantum coding with finite resources’, Nature Communications 7:11419 (2016). arXiv:1504.04617.
Tomamichel, M., Colbeck, R & Renner, R (2009), ‘A fully quantum asymptotic equipartition property’, IEEE Transactions on Information Theory 55(12), 5840–5847. arXiv:0811.1221.
Tomamichel, M., Colbeck, R & Renner, R (2010), ‘Duality between smooth minand max-entropies’, IEEE Transactions on Information Theory 56(9), 4674–4681. arXiv:0907.5238.
Tomamichel, M & Renner, R (2011), ‘Uncertainty relation for smooth entropies’, Physical Review Letters 106(11), 110506. arXiv:1009.2015.
Tomamichel, M & Tan, V.Y.F. (2015), ‘Second-order asymptotics for the classical capacity of image-additive quantum channels’, Communications in Mathematical Physics 338(1), 103–137. arXiv:1308.6503.
Tomamichel, M., Wilde, M. M & Winter, A (2014), ‘Strong converse rates for quantum communication’. arXiv:1406.2946.
Tsirelson, B.S. (1980), ‘Quantum generalizations of Bell's inequality’, Letters in Mathematical Physics 4(2), 93–100.
Tyurin, I.S. (2010), ‘An improvement of upper estimates of the constants in the Lyapunov theorem’, Russian Mathematical Surveys 65(3), 201–202.
Uhlmann, A (1976), ‘The “transition probability” in the state space of a *-algebra’, Reports on Mathematical Physics 9(2), 273–279.
Uhlmann, A (1977), ‘Relative entropy and the Wigner–Yanase–Dyson–Lieb concavity in an interpolation theory’, Communications in Mathematical Physics 54(1), 21–32.
Umegaki, H (1962), ‘Conditional expectations in an operator algebra IV (entropy and information)’, Kodai Mathematical Seminar Reports 14(2), 59–85.
Unruh, W.G. (1995), ‘Maintaining coherence in quantum computers’, Physical Review A 51(2), 992–997. arXiv:hep-th/9406058.
Vedral, V & Plenio, M. B (1998), ‘Entanglement measures and purification procedures’, Physical Review A 57(3), 1619–1633. arXiv:quant-ph/9707035.
von Kretschmann, D (2007), ‘Information Transfer through Quantum Channels’, PhD thesis, Technische Universität Braunschweig.
von Neumann, J (1996), Mathematical Foundations of Quantum Mechanics, Princeton University Press.
Wang, L & Renner, R (2012), ‘One-shot classical–quantum capacity and hypothesis testing’, Physical Review Letters 108(20), 200501. arXiv:1007.5456.
Watrous, J (2015), Theory of Quantum Information. Available at https://cs.uwaterloo.ca/∼watrous/TQI/.
Wehrl, A (1978), ‘General properties of entropy’, Reviews of Modern Physics 50(2), 221–260.
Werner, R.F. (1989), ‘Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model’, Physical Review A 40(8), 4277–4281.
Wiesner, S (1983), ‘Conjugate coding’, SIGACT News 15(1), 78–88.
Wilde, M.M. (2011), ‘Comment on “Secret-key-assisted private classical communication capacity over quantum channels”’, Physical Review A 83(4), 046303.
Wilde, M.M. (2013), ‘Sequential decoding of a general classical–quantum channel’, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 469(2157). arXiv:1303.0808.
Wilde, M.M. (2014), ‘Multipartite quantum correlations and local recoverability’, Proceedings of the Royal Society A 471, 20140941. arXiv:1412.0333.
Wilde, M.M. (2015), ‘Recoverability in quantum information theory’, Proceedings of the Royal Society A 471(2182), 20150338. arXiv:1505.04661.
Wilde, M.M. & Brun, T. A (2008), ‘Unified quantum convolutional coding’, in Proceedings of the IEEE International Symposium on Information Theory, Toronto, Ontario, Canada, pp. 359–363. arXiv:0801.0821.
Wilde, M.M. & Guha, S (2012), ‘Explicit receivers for pure-interference bosonic multiple access channels’, Proceedings of the 2012 International Symposium on Information Theory and its Applications pp. 303–307. arXiv:1204.0521.
Wilde, M.M., Hayden, P, Buscemi, F & Hsieh, M-H. (2012), ‘The informationtheoretic costs of simulating quantum measurements’, Journal of Physics A: Mathematical and Theoretical 45(45), 453001. arXiv:1206.4121.
Wilde, M.M., Hayden, P & Guha, S (2012a), ‘Information trade-offs for optical quantum communication’, Physical Review Letters 108(14), 140501. arXiv:1105.0119.
Wilde, M.M., Hayden, P & Guha, S (2012b), ‘Quantum trade-off coding for bosonic communication’, Physical Review A 86(6), 062306. arXiv:1105.0119.
Wilde, M.M. & Hsieh, M-H. (2010), ‘Entanglement generation with a quantum channel and a shared state’, Proceedings of the 2010 IEEE International Symposium on Information Theory pp. 2713–2717. arXiv:0904.1175.
Wilde, M.M. & Hsieh, M-H. (2012a), ‘Public and private resource trade-offs for a quantum channel’, Quantum Information Processing 11(6), 1465–1501. arXiv:1005.3818.
Wilde, M.M. & Hsieh, M-H. (2012b), ‘The quantum dynamic capacity formula of a quantum channel’, Quantum Information Processing 11(6), 1431–1463. arXiv:1004.0458.
Wilde, M.M., Krovi, H & Brun, T. A (2007), ‘Coherent communication with continuous quantum variables’, Physical Review A 75(6), 060303(R). arXiv:quantph/0612170.
Wilde, M.M., Renes, J. M & Guha, S (2016), ‘Second-order coding rates for pure-loss bosonic channels’, Quantum Information Processing 15(3), 1289–1308. arXiv:1408.5328.
Wilde, M.M. & Savov, I (2012), ‘Joint source-channel coding for a quantum multiple access channel’, Journal of Physics A: Mathematical and Theoretical 45(43), 435302. arXiv:1202.3467.
Wilde, M.M. & Winter, A (2014), ‘Strong converse for the quantum capacity of the erasure channel for almost all codes’, Proceedings of the 9th Conference on the Theory of Quantum Computation, Communication and Cryptography. arXiv:1402.3626.
Wilde, M.M., Winter, A & Yang, D (2014), ‘Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy’, Communications in Mathematical Physics 331(2), 593–622. arXiv:1306.1586.
Winter, A (1999a), ‘Coding theorem and strong converse for quantum channels’, IEEETransactions on Information Theory 45(7), 2481–2485. arXiv:1409.2536.
Winter, A (1999b), ‘Coding Theorems of Quantum Information Theory’, PhD thesis, Universität Bielefeld. arXiv:quant-ph/9907077.
Winter, A (2001), ‘The capacity of the quantum multiple access channel’, IEEETransactions on Information Theory 47(7), 3059–3065. arXiv:quant-ph/9807019.
Winter, A (2004), “‘Extrinsic” and “intrinsic” data in quantum measurements: asymptotic convex decomposition of positive operator valued measures’, Communications in Mathematical Physics 244(1), 157–185. arXiv:quant-ph/0109050.
Winter, A (2007), ‘The maximum output p-norm of quantum channels is not multiplicative for any p > 2’. arXiv:0707.0402.
Winter, A (2015a), ‘Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints’. arXiv:1507.07775.
Winter, A (2015b), ‘Weak locking capacity of quantum channels can be much larger than private capacity’, Journal of Cryptology pp. 1–21. arXiv:1403.6361.
Winter, A & Li, K (2012), ‘A stronger subadditivity relation?’, www.maths.bris.ac. uk/$\sim$csajw/stronger$_$subadditivity.pdf.
Winter, A & Massar, S (2001), ‘Compression of quantum-measurement operations’, Physical Review A 64(1), 012311. arXiv:quant-ph/0012128.
Wolf, M.M., Cubitt, T. S & Perez-Garcia, D (2011), ‘Are problems in quantum information theory (un)decidable?’. arXiv:1111.5425.
Wolf, M.M. & Pérez-García, D (2007), ‘Quantum capacities of channels with small environment’, Physical Review A 75(1), 012303. arXiv:quant-ph/0607070.
Wolf, M.M., Pérez-García, D & Giedke, G (2007), ‘Quantum capacities of bosonic channels’, Physical Review Letters 98(13), 130501. arXiv:quant-ph/0606132.
Wolfowitz, J (1978), Coding theorems of information theory, Springer-Verlag.
Wootters, W.K. & Zurek, W. H (1982), ‘A single quantum cannot be cloned’, Nature 299, 802–803.
Wyner, A.D. (1975), ‘The wire-tap channel’, Bell System Technical Journal 54(8), 1355–1387.
Yard, J (2005), ‘Simultaneous classical–quantum capacities of quantum multiple access channels’, PhD thesis, Stanford University, Stanford, CA. arXiv:quant-ph/0506050.
Yard, J & Devetak, I (2009), ‘Optimal quantum source coding with quantum side information at the encoder and decoder’, IEEE Transactions on Information Theory 55(11), 5339–5351. arXiv:0706.2907.
Yard, J., Devetak, I & Hayden, P (2005), ‘Capacity theorems for quantum multiple access channels’, in Proceedings of the International Symposium on Information Theory, Adelaide, Australia, pp. 884–888. arXiv:cs/0508031.
Yard, J., Hayden, P & Devetak, I (2008), ‘Capacity theorems for quantum multipleaccess channels: Classical–quantum and quantum–quantum capacity regions’, IEEETransactions on Information Theory 54(7), 3091–3113. arXiv:quant-ph/0501045.
Yard, J., Hayden, P & Devetak, I (2011), ‘Quantum broadcast channels’, IEEETransactions on Information Theory 57(10), 7147–7162. arXiv:quant-ph/0603098.
Ye, M-Y., Bai, Y-K. & Wang, Z. D (2008), ‘Quantum state redistribution based on a generalized decoupling’, Physical Review A 78(3), 030302. arXiv:0805.1542.
Yen, B.J. & Shapiro, J. H (2005), ‘Multiple-access bosonic communications’, Physical Review A 72(6), 062312. arXiv:quant-ph/0506171.
Yeung, R.W. (2002), A First Course in Information Theory, Information Technology: Transmission, Processing, and Storage, Springer (Kluwer Academic/Plenum Publishers), New York, NY.
Zhang, L (2014), ‘A lower bound of quantum conditional mutual information’, J. Phys. A: Math. Theor. 47(2014) 415303. arXiv:1403.1424.
Zhang, Z (2007), ‘Estimating mutual information via Kolmogorov distance’, IEEE Transactions on Information Theory 53(9), 3280–3282.
Zurek, W.H. (2000), ‘Einselection and decoherence from an information theory perspective’, Annalen der Physik 9(11–12), 855–864. arXiv:quant-ph/0011039.

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