Comparisons between quantum state distinguishability measures

TL;DR

This paper compiles and proves the sharpest inequalities between various quantum state distinguishability measures, including known and new results, with cases of equality to validate their optimality.

Contribution

It provides a comprehensive collection of the tightest inequalities between quantum distinguishability measures, including new proofs and inequalities.

Findings

Established sharp bounds between quantum distinguishability measures

Presented new inequalities and generalized existing ones

Provided cases of equality to confirm the bounds' optimality

Abstract

We provide a compendium of inequalities between several quantum state distinguishability measures. For each measure these inequalities consist of the sharpest possible upper and lower bounds in terms of another measure. Some of these inequalities are already known, but new or more general proofs are given, whereas other inequalities are new. We also supply cases of equality to show that all inequalities are indeed the sharpest possible.