Unambiguous state discrimination with intrinsic coherence

TL;DR

This paper explores the discrimination of quantum states, revealing conditions under which pure or mixed states are more effectively distinguished, and how coherence impacts success probabilities across different system dimensions.

Contribution

It provides a comparative analysis of pure-pure, pure-mixed, and mixed-mixed state discrimination, highlighting the role of coherence and extending findings to infinite-dimensional systems.

Findings

Pure-pure discrimination outperforms mixed cases under equal-fidelity.

Coherence in pure states can hinder discrimination in low dimensions.

In infinite dimensions, coherence effects on discrimination can reverse.

Abstract

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa.