No Access

Around Shannon's interpretation for entropy-preserving stochastic averages

Marie Choda

Osaka Kyoiku University, Asahigaoka, Kashiwara 582-8582, Japan

https://doi.org/10.1142/S0129167X14500967Cited by:5 (Source: Crossref)

Abstract

Let Φ be a positive unital Tr-preserving map on M_n(ℂ). We give various characterizations for Φ to preserve the von Neumann entropy of a state ρ on M_n(ℂ). Among others, it is given by that Φ behaves to ρ as a *-automorphism. This is also equivalent to that the entropy of the stochastic matrix arising from {ρ, Φ} is zero.

Keywords:

AMSC: 46L55, 46L37, 46L40

References

M. D. Choi , J. Math. 18 , 565 ( 1974 ) . Google Scholar
F. Hiai et al. , Rep. Math. Phys. 23 , 691 ( 2011 ) . Link, Web of Science, Google Scholar
S. Neshveyev and E. Størmer , Dynamical Entropy in Operator Algebras ( Springer-Verlag , Berlin , 2006 ) . Crossref, Google Scholar
M. Ohya and D. Petz , Quantum Entropy and Its Use , Texts and Monographs in Physics ( Springer-Verlag , Berlin , 1993 ) . Crossref, Google Scholar
D. Petz , Quantum Information Theory and Quantum Statistics , Theoretical and Mathematical Physics ( Springer , Berlin, Heidelberg , 2008 ) . Google Scholar
A. B. Poritz and J. A. Poritz , Linear Algebra Appl. 434 , 1425 ( 2011 ) . Crossref, Web of Science, Google Scholar
C. E. Shannon , Bell Syst. Tech. 27 , 379 ( 1948 ) . Crossref, Web of Science, Google Scholar
E. Størmer , Positive Linear Maps of Operator Algebras ( Springer SMM , Berlin, Heidelberg , 2013 ) . Crossref, Google Scholar
L. Zhang and J. Wu , Phys. Lett. A 375 , 4163 ( 2011 ) . Crossref, Web of Science, Google Scholar
K. Życzkowski et al. , J. Phys. A 36 , 3425 ( 2003 ) . Crossref, Google Scholar