Classical pair of states as optimal pair for quantum distinguishability quantifiers

TL;DR

This paper demonstrates that the pairs of states that maximize quantum distinguishability quantifiers are orthogonal, classical states, due to the contractivity property under quantum operations, impacting quantum dynamics analysis.

Contribution

It establishes that maximal quantum distinguishability is achieved by orthogonal, classical state pairs, clarifying the nature of optimal pairs in quantum state discrimination.

Findings

Maximal distinguishability pairs are orthogonal states.

Contractivity under quantum maps constrains optimal pairs.

Classical states are optimal for quantum distinguishability quantifiers.

Abstract

The capability to quantitatively distinguish quantum states is of great importance for a variety of tasks, and has recently played an important role in the study of quantum reduced dynamics and their characterization in terms of memory effects. A crucial property of quantum distinguishability quantifiers considered in the latter framework is the contractivity under the action of completely positive trace-preserving maps. We show that this requirement warrants that the pairs on which these quantifiers attain their maximal value are pairs of orthogonal, and in this sense classical, states.