The quantum capacity with symmetric side channels

IEEE Transactions on Information Theory

Volumn 54, Issue 9, 2008, Pages 4208-4217

  Smith, Graeme ^a,b   Smolin, John A ^b   Winter, Andreas ^c  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

^c UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

Entanglement; Quantum channel capacity; Quantum communication

Indexed keywords

ENTANGLEMENT; QUANTUM CHANNEL CAPACITY; QUANTUM COMMUNICATION; SIDE CHANNELS;

CHANNEL CAPACITY;

EID: 51349117868     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.928269     Document Type: Article

References (35)

1. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423, 623-656, 1948.
2. T. M. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
3. S. Lloyd, "Capacity of the noisy quantum channel," Phys. Rev. A, Gen. Phys., vol. 55, pp. 1613-1622, 1997.
4. P. W. Shot, "The quantum channel capacity and coherent information," in Lecture Notes, MSRI Workshop Quantum Comput., 2002 [Online]. Available: http://www.msri.org/publications/ln/msri/2002/quantumcrypto/shor/1/
5. I. Devetak, "The private classical capacity and quantum capacity of a quantum channel," IEEE Trans. Inf. Theory, vol. 51, no. 1, pp. 44-55, Jan. 2005.
6. V. Giovannetti and R. Fazio, "Information-capacity description of spinchain correlations," Phys. Rev. A, Gen. Phys., vol. 71, p. 032314, 2005.
7. E. M. Rains, "Bound on distillable entanglement," Phys. Rev. A, Gen. Phys., vol. 60, pp. 179-184, 1999.
8. C. H. Bennett, D. P. DiVincenzo, and J. A. Smolin, "Capacities of quantum erasure channels," Phys. Rev. Lett., vol. 78, no. 16, pp. 3217-3220, Apr. 1997.
9. C. H. Bennett, P. W. Shor, J. A. Smolin, and A. V. Thapliyal, "Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem," IEEE Trans. Inf. Theory, vol. 48, no. 10, pp. 2637-2655, Oct. 2002.
10. C. Adami and N. Cerf, "Von Neumann capacity of noisy quantum channels," Phys. Rev. A, Gen. Phys., pp. 3470-3483, 1997.
11. J. A. Smolin, F. Verstraete, and A. Winter, "Entanglement of assistance and multipartite state distillation," Phys. Rev. A, Gen. Phys., vol. 72, p. 052317, 2005.
12. A. Winter, "On environment-assisted capacities of quantum channels," [OUline]. Available: http://arXiv:quant-ph/0507045
13. B. Schumacher and M. A. Nielsen, "Quantum data processing and error correction," Phys. Rev. A, Gen. Phys., vol. 54, p. 2629, 1996.
14. D. DiVincenzo, P. W. Shot, and J. A. Smolin, "Quantum channel capacity of very noisy channels," Phys. Rev. A, Gen. Phys., vol. 57, no. 2, pp. 830-839, 1998.
15. P. W. Shor and J. A. Smolin, "Quantum error-correcting codes need not completely reveal the error syndrome," 1996 [Online]. Available: http://arXiv:qUant-ph/9604006
16. G. Smith and J. A. Smolin, "Degenerate quantum codes for Pauli channels," Phys. Rev. Lett., vol. 98, p. 030501, 2007.
17. D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Macchiavello, and J. A. Smolin, "Optimal universal and state-dependent quantum cloning," Phys. Rev. A, vol. 57, p. 2368, 1998.
18. N. J. Cerf, "Quantum cloning and the capacity of the Pauli channel," Phys. Rev. Lett., vol. 84, p. 4497, 2000.
19. E. M. Rains, "A semidefinite program for distillable entanglement," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2921-2933, Nov. 2001.
20. V. Vedral and M. B. Plenio, Phys. Rev. A, Gen. Phys., vol. 57, p. 1619, 1998.
21. H. Barnum, E. Knill, and M. A. Nielsen, "On quantum fidelities and channel capacities," IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 1317-1329, Jul. 2000.
22. I. Devetak and P. W. Shor, "The capacity of a quantum channel for simultaneous transmission of classical and quantum information," Commun. Math. Phys., vol. 256, pp. 287-303, 2005.
23. C. H. Bennett, A. W. Harrow, D. W. Leung, and J. A. Smolin, "On the capacities of bipartite Hamiltonians and unitary gates," IEEE Trans. Inf. Theory, vol. 49, no. 8, pp. 1895-1911, Aug. 2003.
24. M. Christandl and A. Winter, ""Squashed entanglement": An additive entanglement measure," J. Math. Phys., vol. 45, no. 3, pp. 829-840, 2004.
25. C. A. Fuchs and J. van de Graaf, "Cryptographic distinguishability measures for quantum mechanical states," IEEE Trans. Inf. Theory, vol. 45, pp. 1216-1227, 1999.
26. W. F. Stinespring, "Positive functions on C*-algebras," Proc. Amer. Math. Soc., vol. 6, pp. 211-216, 1955.
27. E. H. Lich and M.-B. Ruskai, "Proof of the strong subadditivity of quantum-mechanical entropy," J. Math. Phys., vol. 14, no. 12, pp. 1938-1941, 1973.
28. H. N. Barnum, M. A. Nielsen, and B. Schumacher, "Information transmission through a noisy quantum channel," Phys. Rev. A, Gen. Phys., vol. 57, no. 6, pp. 4153-4175, 1998.
29. M. Fannes, "A continuity property of the entropy density of spin lattice systems," Commun. Math. Phys., vol. 31, pp. 291-294.
30. G. Lindblad, "Completely positive maps and entropy inequalities," Commun. Math. Phys., vol. 40, pp. 147-151, 1975.
31. P. W. Shot, J. A. Smolin, and B. M. Terhal, "Nonadditivity of bipartite distillable entanglement follows from a conjecture on bound entangled Werner states," Phys. Rev. Lett., vol. 86, pp. 2681-2684, 2000.
32. D. P. DiVincenzo, P. W. Shot, J. A. Smolin, B. M. Terhal, and A. V. Thapliyal, "Evidence for bound entangled states with negative partial transpose," Phys. Rev. A, Gen. Phys., vol. 61, p. 062312, 2000.
33. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, "Mixed state entanglement and quantum error correction," Phys. Rev. A, Gen. Phys., vol. 54, pp. 3824-3851, 1996.
34. B. Kraus, N. Gisin, and R. Renner, "Lower and upper bounds on the secret key rate for quantum key distribution protocols using one-way classical communication," Phys. Rev. Lett., vol. 95, p. 080501, 2005.
35. R. Renner, N. Gisin, and B. Kraus, "Information-theoretic security proof for quantum-key-distribution protocols," Phys. Rev. A, Gen. Phys., vol. 72, p. 012332, 2005.