A remainder term for Hölder’s inequality for matrices and quantum entropy inequalities

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Abstract

We prove a sharp remainder term for Hölder’s inequality for traces as a consequence of the uniform convexity properties of the Schatten trace norms. We then show how this implies a novel family of Pinsker type bounds for the quantum Rényi entropy. Finally, we show how the sharp form of the usual quantum Pinsker inequality for relative entropy may be obtained as a fairly direct consequence of uniform convexity.

Original languageEnglish (US)
Pages (from-to)365-371
Number of pages7
JournalArchiv der Mathematik
Volume109
Issue number4
DOIs
StatePublished - Oct 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Density matrix
  • Entropy
  • Uniform convexity

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