Smooth entropies and the quantum information spectrum

IEEE Transactions on Information Theory

Volumn 55, Issue 6, 2009, Pages 2807-2815

  Datta, Nilanjana ^a   Renner, Renato ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b ETH ZURICH   (Switzerland)

Author keywords

Information spectrum; Randomness extraction; Smooth entropies; Spectral entropy rates

Indexed keywords

ASYMPTOTIC LIMITS; ENTROPY MEASURE; INFORMATION SPECTRUM; QUANTUM INFORMATION; QUANTUM SETTING; RANDOMNESS EXTRACTION; SHANNON ENTROPY; SMOOTH ENTROPIES; SOURCE-CODING; SPECTRAL ENTROPY; SPECTRAL ENTROPY RATES; VON NEUMANN ENTROPY;

CHANNEL CODING; INFORMATION THEORY; QUANTUM OPTICS;

ENTROPY;

EID: 66949111858     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2018340     Document Type: Article

References (31)

1. T. S. Han, Information-Spectrum Methods in Information Theory. New York: Springer-Verlag, 2002.
2. T. S. Han and S. Verdú, "Approximation theory of output statistics," IEEE Trans. Inf. Theory, vol. 39, pp. 752-772, 1993.
3. S. Verdú and T. S. Han, "A general formula for channel capacity," IEEE Trans. Inf. Theory, vol. 40, pp. 1147-1157, 1994.
4. H. Nagaoka and M. Hayashi, "An information-spectrum approach to classical and quantum hypothesis testing for simple hypotheses," IEEE Trans. Inf. Theory, vol. 53, pp. 534-549, 2007.
5. T. Ogawa and H. Nagaoka, "Strong converse and stein's lemma in quantum hypothesis testing," IEEE Trans. Inf. Theory, vol. 46, pp. 2428-2433, 2000.
6. M. Hayashi, "General formulas for fixed-length quantum entanglement concentration," IEEE Trans. Inf. Theory, vol. 52, 2006.
7. M. Hayashi and H. Nagaoka, "General formulas for capacity of classical-quantum channels," IEEE Trans. Inf. Theory, vol. 49, pp. 1753-1768, 2003.
8. G. Bowen and N. Datta, "Beyond I.I.D. in quantum information theory," in Proc. 2006 IEEE Int. Symp. Inf. Theory, 2006, arXiv:qUant-ph/0604013.
9. G. B. Datta, Quantum Coding Theorems for Arbitrary Sources, Channels and Entanglement Resources 2006, arXiv:qUant-ph/0610003.
10. G. Bowen and N. Datta, "Asymptotic entanglement manipulation of bipartite pure states," IEEE Trans. Inf. Theory, vol. 54, pp. 3677-3686, 2008.
11. G. Bowen and N. Datta, Entanglement Cost for Sequences of Arbitrary Quantum States 2007, arXiv:0704.1957.
12. K. Matsumoto, Entanglement Cost and Distillable Entanglement of Symmetric States 2007, arXiv:0708.3129.
13. C. H. Bennett, G. Brassard, C. Crépeau, and U. Maurer, "Generalized privacy amplification," IEEE Trans. Inform. Theory, vol. 41, pp. 1915-1923, 1995.
14. A. Rényi, "On measures of entropy and information," in Proc. 4th Berkeley Symp. Math. Stat. Prob., 1961, vol. 1, pp. 547-561.
15. C. Cachin, "Smooth entropy and Rényi entropy," in Adv. Crypt. - EUROCRYPT '97. : Springer, 1997, vol. LNCS, 1233, pp. 193-208.
16. R. Renner and S. Wolf, "Smooth Rényi entropy and applications," in Proc. Int. Symp. Inf. Theory, 2004, pp. 233. IEEE-233. IEEE.
17. R. Renner, "Security of Quantum Key Distribution," Ph.D., ETH Zurich, Zurich, Switzerland, 2005.
18. R. Renner and R. König, "Universally composable privacy amplification against quantum adversaries," in Proc. TCC 2005. New York: Springer, 2005, vol. 3378, LNCS.
19. R. Renner and S. Wolf, "Simple and tight bounds for information reconciliation and privacy amplification," in Adv. Crypt. - ASIACRYPT 2005. : Springer, 2005, vol. LNCS, 3788, pp. 199-216.
20. R. Renner, S. Wolf, and J. Wullschleger, "Trade-offs in information-theoretic multi-party one-way key agreement," in Proc. of ICITS 2007, 2007.
21. I. Damgård, S. Fehr, R. Renner, L. Salvail, and C. Schaffner, "A tight high-order entropic uncertainty relation with applications," in Adv. Crypt. - CRYPTO 2007. New York: Springer, 2007, vol. 4622, LNCS, pp. 360-378.
22. I. Damgård, S. Fehr, L. Salvail, and C. Schaffner, "Cryptography in the bounded quantum-storage model," in Proc. 46th Annu. Symp. Found. Comput. Sci. (FOCS), 2005, pp. 449-458.
23. I. Damgård, S. Fehr, L. Salvail, and C. Schaffner, "Secure identification and QKD in the bounded-quantum-storage model," in Advances in Cryptology - CRYPTO 2007. New York: Springer, 2007, vol. 4622, pp. 342-359.
24. B. Schoenmakers, J. Tijoelker, P. Tuyls, and E. Verbitskiy, Smooth Rényi Entropy of Ergodic Quantum Information Sources 2007, arXiv:0704.3504.
25. V. Scarani and R. Renner, Quantum Cryptography With Finite Resources 2007, arXiv:0708.0709.
26. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U.K.: Cambridge University Press, 2000.
27. A. Winter, "Coding theorem and strong converse for quantum channels," IEEE Trans. Inf. Theory, vol. 45, 1999.
28. T. Ogawa and H. Nagaoka, New Proof of the Channel Coding Theorem Via Hypothesis Testing in Quantum Information Theory 2002, arXiv:qUant-ph/ 0208139.
29. R. Impagliazzo, L. A. Levin, and M. Luby, "Pseudo-random generation from one-way functions," in Proc. Twenty-First Annu. ACM Symp. Theory Comput., 1989, pp. 12-24.
30. C. H. Bennett, G. Brassard, and J. M. Robert, "Privacy amplification by public discussion," SIAM J. Comput., vol. 17, pp. 210-229, 1988.
31. R. Bhatia, Matrix Analysis. New York: Springer, 1997.