Reverse Test and Characterization of Quantum Relative Entropy

2010/10/05 by Keiji Matsumoto, Matsumoto, Keiji · 2 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1010.1030

openalex publication_date 2010/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the upperbound and the lowerbund of D^Q(ρ||σ) is D^R(ρ||σ) :=tr% ρln√ρσ^-1√ρ and D(ρ||σ) := tr ρ(lnρ-lnσ) , respectively. In the latter setting, we prove uniqueness of quantum relative entropy, that is, D^Q(ρ||σ) should equal a constant multiple of D(ρ||σ) . In the analysis, we define and use reverse test and asymptotic reverse test, which are natural inverse of hypothesis test.

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