Weak quasi-factorization for the Belavkin-Staszewski relative entropy

Abstract

Quasi-factorization-type inequalities for the relative entropy have recently proven to be fundamental in modern proofs of modified logarithmic Sobolev inequalities for quantum spin systems. In this paper, we show some results of weak quasi-factorization for the Belavkin-Staszewski relative entropy, i.e. upper bounds for the BS-entropy between two bipartite states in terms of the sum of two conditional BS-entropies, up to some multiplicative and additive factors.

arXiv comment12 pages, 1 figure

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Cited by in corpus (3)

• Exponential decay of mutual information for Gibbs states of local Hamiltonians
• Continuity of quantum entropic quantities via almost convexity
• Quasi-factorization and Multiplicative Comparison of Subalgebra-Relative Entropy