Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

Fumio Hiai, D. Petz

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Given a positive function f on (0, ∞) and a non-zero real parameter θ, we consider a function Iθf(A,B,X) = tr X*(f(LAR-1B)RB)(X)in three matrices A, B > 0 and X. This generalizes the notion of monotone metrics on positive definite matrices, and in the literature θ = ±1 has been typical. We investigate how operator monotony of f is sufficient and/or necessary for joint convexity/concavity of Iθf(A,B,X). Similar discussions are given for quasi-entropies and quantum skew informations.

Original languageEnglish
Article number062201
JournalJournal of Mathematical Physics
Volume54
Issue number6
DOIs
Publication statusPublished - Jun 3 2013

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convexity
Convexity
monotony
theorems
Entropy
entropy
concavity
Positive definite matrix
Concavity
matrices
Theorem
Skew
Monotone
Sufficient
operators
Metric
Generalise
Necessary
Operator

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Convexity of quasi-entropy type functions : Lieb's and Ando's convexity theorems revisited. / Hiai, Fumio; Petz, D.

In: Journal of Mathematical Physics, Vol. 54, No. 6, 062201, 03.06.2013.

Research output: Contribution to journalArticle

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