MONOTONICITY OF QUANTUM RELATIVE ENTROPY REVISITED

2002/09/06 by D. Petz, DÉNES PETZ · 9 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Generalized relative entropy #Kullback–Leibler divergence #Monotonic function #Property (philosophy) #Quantum #Quantum Information and Cryptography #Quantum discord #Quantum operation #Quantum relative entropy #Statistical Mechanics and Entropy #Von Neumann architecture #Von Neumann entropy #quant-ph

paper · pdf · doi:10.1142/s0129055x03001576

published as Rev. Math. Phys. 15(2003), 79--91. · 13 pages, LATEX file

arxiv created 2002/09/06 · openalex publication_date 2003/02/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden–Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly indicated.

Citations

• Completely positive maps and entropy inequalities

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