ON AN INEQUALITY CONJECTURED BY BESENYEI AND PETZ

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Ileri A., DEMİR S.

OPERATORS AND MATRICES, vol.16, no.2, pp.299-307, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.7153/oam-2022-16-23
  • Journal Name: OPERATORS AND MATRICES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.299-307
  • Keywords: Tsallis entropy, partial subadditivity, trace inequalities
  • Open Archive Collection: AVESIS Open Access Collection
  • Dokuz Eylül University Affiliated: Yes

Abstract

In this paper we investigate the inequality Tr(T circle times I-2)rho(12)( log(q)rho(12) - log(q)rho(1)circle times I-2 - I-1 circle times log(q)rho(2)) >= 0, where rho(12) is a density matrix and 0 <= T is an element of M-m(C). This inequality was conjectured by Besenyei and Petz in 2013, where it was proved to hold for the density matrices in M-2(C) circle times M-2(C). Here we prove this inequality for the density matrices in M-m(C) circle times M-n(C) using some elementary matrix methods. We also obtain some new inequalities related to the operators (matrices) in this inequality.