ON AN INEQUALITY CONJECTURED BY BESENYEI AND PETZ

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Ileri A., DEMİR S.

OPERATORS AND MATRICES, cilt.16, sa.2, ss.299-307, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.7153/oam-2022-16-23
  • Dergi Adı: OPERATORS AND MATRICES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.299-307
  • Anahtar Kelimeler: Tsallis entropy, partial subadditivity, trace inequalities
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.