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| related topics |
| {information, entropy, channel} |
| {let, theorem, proof} |
| {observables, space, algebra} |
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| {group, space, representation} |
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Inequalities for Quantum Entropy: A Review with Conditions for Equality
Mary Beth Ruskai
abstract: This paper presents self-contained proofs of the strong subadditivity
inequality for quantum entropy and some related inequalities for the quantum
relative entropy, most notably its convexity and its monotonicity under
stochastic maps. Moreover, the approach presented here, which is based on
Klein's inequality and one of Lieb's less well-known concave trace functions,
allows one to obtain conditions for equality. Using the fact that the Holevo
bound on the accessible information in a quantum ensemble can be obtained as a
consequence of the monotonicity of relative entropy, we show that equality can
be attained for that bound only when the states in the ensemble commute. The
paper concludes with an Appendix giving a short description of Epstein's
elegant proof of the relevant concavity theorem of Lieb.
- oai_identifier:
- oai:arXiv.org:quant-ph/0205064
- categories:
- quant-ph math-ph math.MP
- comments:
- 28 pages, latex Added reference to M.J.W. Hall, "Quantum Information
and Correlation Bounds" Phys. Rev. A, 55, pp 100--112 (1997)
- doi:
- 10.1063/1.1497701
- arxiv_id:
- quant-ph/0205064
- journal_ref:
- J. Math. Phys. 43, 4358-4375 (2002); erratum 46, 019901 (2005).
- created:
- 2002-05-12
- updated:
- 2002-05-19
Full article ▸
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