Remarks on on Kim's Strong Subadditivity Matrix Inequality: Extensions and Equality Conditions

TL;DR

This paper discusses extensions of Kim's matrix inequality related to strong subadditivity, exploring new inequalities and their equality conditions in bipartite and tripartite quantum systems.

Contribution

It introduces new matrix inequalities derived from operator convex functions and analyzes their equality conditions, extending Kim's previous work.

Findings

New matrix inequalities for bipartite and tripartite systems.

Equality conditions similar to strong subadditivity.

Additional examples illustrating the inequalities.

Abstract

We describe recent work of Kim in arXiv:1210.5190 to show that operator convex functions associated with quasi-entropies can be used to prove a large class of new matrix inequalities in the tri-partite and bi-partite setting by taking a judiciously chosen partial trace over all but one of the spaces. We give some additional examples in both settings. Furthermore, we observe that the equality conditions for all the new inequalities are essentially the same as those for strong subadditivity.