Rényi extrapolation of Shannon entropy

Open Systems and Information Dynamics

Volumn 10, Issue 3, 2003, Pages 297-310

  Życzkowski, Karol ^a,b  

^a JAGIELLONIAN UNIVERSITY   (Poland)

^b CENTER FOR THEORETICAL PHYSICS   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347585673     PISSN: 12301612     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025128024427     Document Type: Article

References (25)

1. C. Shannon, Mathematical theory of communication, Bell System Tech. J. 27, 379, 623 (1948)
2. A. I. Khinchin, Mathematical Foundations of Information Theory, Dover, 1957.
3. A. Rényi, On measures of entropy and information, in: Proc. Fourth. Berkeley Symp. Math. Stat. Prob. 1960, Vol. I, University of California Press, Berkeley, 1961, p. 547.
4. J. N. Kapur, Measures of Information and Their Applications, John Wiley & Sons, New York, 1994.
5. C. Arndt. Information Measures: Information and its Description in Science and Engineering, Springer, Berlin, 2001.
6. P. Horodecki and A. Ekert, Direct detection of quantum entanglement, Phys. Rev. Lett. 89, 127902 (2002).
7. C. M. Alves, P. Horodecki, D. K. L. Oi, L. C. Kwek, and A. K. Ekert, Direct estimation of functionals of density operators by local operations and classical communication, preprint quant-ph/0304123.
8. A. Bialas and W. Czyż, Renyi entropies in multiparticle production, Acta Phys. Pol. B 31, 2803 (2000).
9. A. Bialas, W. Czyż, and A. Ostruszka, Renyi entropies in particle cascades, Acta Phys. Pol. B 34, 69 (2003).
10. J. Pipek and I. Varga, Universal scheme for the spacial-localization properties of one-particle states infinite d-dimensional systems, Phys. Rev. A 46, 3148 (1992).
11. I. Varga and J. Pipek, On Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems, arXiv preprint: cond-mat/0204041.
12. K. Życzkowski and I. Bengtsson, Relativity of pure states entanglement, Ann. Phys. (N.Y.) 295, 115 (2002).
13. T.-C. Wei, K. Nemoto, P. M. Goldbart, P. G. Kwiat, W. J. Munro, and F. Verstraete, Maximal entanglement versus entropy for mixed quantum states, Phys. Rev. A 67, 022110 (2003).
14. F. Topsøe, Some inequalities for information divergence and related measures of discrimination, IEEE Trans. Inform. Theory 46, 1602 (2000).
15. P. Harremoës and F. Topsøe, Inequalities between entropy and index of coincidence derived from information diagrams, IEEE Trans. Inform. Theory 47, 2944 (2001).
16. C. Beck and F. Schlögl, Thermodynamics of chaotic systems, Cambridge University Press, Cambridge, 1993.
17. D. W. Berry and B. C. Sanders, Bounds on entropy, preprint arXiv quant-ph/0305059.
18. F. Topsøe, Entropy and index of coincidence, lower bounds, preprint, Copenhagen, 2003.
19. P. Harremoës, preprint, Copenhagen, 2003.
20. R. A. Fisher, Theory of Statistical Estimation, Proc. Cambridge Philos. Soc. 22, 700 (1925).
21. J. Havrda and F. Charvat, Quantification methods of classification processes: Concept of structural α-entropy, Kybernetica 3, 30 (1967).
22. Z. Daroczy, Inf. Control 16, 36 (1970).
23. C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys. 52, 479 (1988).
24. A. Wehrl, General properties of entropy, Rev. Mod. Phys. 50, 221 (1978).
25. S. Gnutzmann and K. Życzkowski, Ŕnyi-Wehrl entropies as measures of localization in phase space, J. Phys. A 34, 10123 (2001).