A trace inequality arising from quantum information theory
type: Item
instance of: scholarly article
title: A trace inequality arising from quantum information theory
zbMATH Open document ID: 1078.15015
author: Jun-Ichi Fujii
published in: Linear Algebra and its Applications
publication date: 2005-06-01T00:00:00Z
review text: The author introduces another informational quantity for real-valued (continuous) functions \(f\) and \(g\): \[ S_{f,g}(A,x)=T_r f(A)Xg(A)X-T_r f(A)g(A)X^2 \] for selfadjoint matrices \(A\) and \(X\) which is an extension of \textit{E. H. Lieb}'s skew information [Adv. Math. 11, 267--288 (1973; Zbl 0267.46055)]. Conditions for \(f\) and \(g\) such that \(S_{f,g}(A,x)\) should be negative or positive, are given. As applications, the problem posed by \textit{K. Yanagi, S. Furuichi} and \textit{K. Kuriyama} [Linear Algebra Appl. 395, 351--359 (2005; Zbl 1067.94006)] from quantum information theory is settled.
reviewed by: Costică Moroşanu
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 94A15
zbMATH DE Number: 2173021
zbMATH Keywords: trace inequality
zbMATH Keywords: skew information
zbMATH Keywords: Jensen's inequality
zbMATH Keywords: selfadjoint matrices
zbMATH Keywords: quantum information theory
MaRDI profile type: Publication
full work available at URL: j.laa.2004.11.009
OpenAlex ID: W1981019056
cites work: Trace inequalities for multiple products of two matrices
cites work: Some inequalities for norms on matrices and operators
cites work: Reliability function of general classical-quantum channel
cites work: Convex trace functions and the Wigner-Yanase-Dyson conjecture
cites work: On trace inequalities and their applications to noncommutative communication theory
DOI: 10.1016/J.LAA.2004.11.009
description: scientific article; zbMATH DE number 2173021