Weak quasi-factorization for the Belavkin-Staszewski relative entropy

TL;DR

This paper establishes weak quasi-factorization inequalities for the Belavkin-Staszewski relative entropy, providing bounds that relate bipartite state entropies to conditional entropies, which are important for quantum spin system analysis.

Contribution

It introduces new weak quasi-factorization bounds for the Belavkin-Staszewski relative entropy, extending the theoretical framework for quantum entropy inequalities.

Findings

Derived upper bounds for the BS-entropy between bipartite states

Established relationships between bipartite and conditional BS-entropies

Extended the applicability of quasi-factorization inequalities in quantum information

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.