A fully quantum asymptotic equipartition property

IEEE Transactions on Information Theory

Volumn 55, Issue 12, 2009, Pages 5840-5847

  Tomamichel, Marco ^a   Colbeck, Roger ^a   Renner, Renato ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Asymptotic equipartition property; Quantum information; R nyi entropies; Smooth entropies; Von Neumann entropy

Indexed keywords

CONDITIONAL ENTROPY; EQUIPARTITION; EXPLICIT BOUNDS; OUTPUT SEQUENCES; QUANTUM INFORMATION; SIDE INFORMATION; SMOOTH ENTROPIES; VON NEUMANN ENTROPY;

ASYMPTOTIC ANALYSIS; QUANTUM OPTICS;

ENTROPY;

EID: 77949536061     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2032797     Document Type: Article

References (25)

1. T. M. Cover and J. A. Thomas, Elements of Information Theory., ser. Series in Telecommunications. New York: Wiley, 1991.
2. T. Holenstein and R. Renner, On the Randomness of Independent Experiments 2006 [Online]. Available: http://arxiv.org/abs/cs/0608007
3. R. Renner and S. Wolf, "Smooth Rényi entropy and applications," in Proc. ISIT, 2004.
4. A. Rényi, "On measures of information and entropy," in Proc. 4th Berkeley Symp. on Math., Stat. and Prob., 1961, pp. 547-561.
5. R. Jozsa and B. Schumacher, "A new proof of the quantum noiseless coding theorem," J. Mod. Opt., vol.41, pp. 2343-2349, 1994.
6. H. Barnum, E. Knill, and M. Nielsen, "On quantum fidelities and channel capacities," IEEE Trans. Inf. Theory, vol.46, no.4, pp. 1317-1329, Jul. 2000.
7. B. Schoenmakers, J. Tjoelker, P. Tuyls, and E. Verbitskiy, "Smooth Rényi entropy of ergodic quantum information sources," in Proc. ISIT, 2007, pp. 256-260.
8. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information.. Cambridge, U.K.: Cambridge University Press, 2000.
9. R. Renner, "Security of Quantum Key Distribution" Ph.D. dissertation, ETH, Zurich, 2005 [Online]. Available: http://arxiv.org/abs/quant- ph/0512258
10. F. Hiai and D. Petz, "The proper formula for relative entropy and its asymptotics in quantum probability," Commun. Math. Phys., vol.143, pp. 99-114, 1991.
11. T. Ogawa and H. Nagaoka, "Strong converse and Stein's lemma in quantum hypothesis testing," IEEE Trans. Inf. Theory, vol.46, pp. 2428-2433, Nov. 2000.
12. M. Hayashi, Quantum Information-An Introduction.. New York: Springer, 2006.
13. R. Renner and R. König, "Universally composable privacy amplification against quantum adversaries," in Proc. TCC, 2005, pp. 407-425 [Online]. Available: http://arxiv.org/abs/quant-ph/0403133
14. R. König, R. Renner, and C. Schaffner, The Operational Meaning of min- and max-Entropy July 2008 [Online]. Available: http://arxiv.org/abs/0807. 1338
15. A. Gilchrist, N. K. Langford, and M. A. Nielsen, "Distance measures to compare real and ideal quantum processes," Aug. 2004 [Online]. Available: http://arxiv.org/abs/quant-ph/0408063
16. M. Tomamichel, R. Colbeck, and R. Renner, "Duality between smooth min- and max-entropies," [Online]. Available: http:\\arxiv.org/abs/0907. 5238, 2009.
17. K. M. R. Audenaert, J. Calsamiglia, R. Munoz-Tapia, E. Bagan, L. Masanes, A. Acin, and F. Verstraete, "Discriminating states: The quantum chernoff bound," Phys. Rev. Lett., vol.98, no.16, p. 160501, 2007.
18. M. Ohya and D. Petz, Quantum Entropy and Its Use. New York: Springer, 1993.
19. M. Mosony and N. Datta, Generalized Relative Entropies and the Capacity of Classical-Quantum Channels 2008 [Online].Available: http://arxiv.org/abs/ 0810.3478
20. R. Bhatia, Matrix Analysis, ser. Graduate Texts in Mathematics.. : Springer, 1997.
21. N. Datta, Min- and Max- Relative Entropies and a New Entanglement Monotone Mar. 2008 [Online]. Available: http://arxiv.org/abs/0803. 2770v1
22. R. Alicki and M. Fannes, Continuity of Quantum Mutual Information Dec. 2003 [Online]. Available: http://arxiv.org/abs/quant-ph/0312081v1
23. F. Hansen and G. K. Pedersen, "Jensen's operator inequality," Bull. London Math. Soc., vol.35, no.5, pp. 553-564, Jul. 2003.
24. D. Petz, "Quasi-entropies for finite quantum systems," Rep. Math. Phys., vol.23, no.1, pp. 57-65, Sept. 1984.
25. N. Datta and R. Renner, Smooth Rényi Entropies and the Quantum Information Spectrum Jan. 2008 [Online]. Available: http://arxiv.org/abs/0801. 0282