Entanglement witness and multipartite quantum state discrimination

TL;DR

This paper explores the connection between entanglement witnesses and the problem of multipartite quantum state discrimination, providing conditions and methods to analyze and construct ensembles with nonlocality in discrimination.

Contribution

It establishes a novel link between entanglement witnesses and minimum-error discrimination by separable measurements, offering new criteria and construction methods.

Findings

Derived necessary and sufficient conditions for separable measurement discrimination

Provided bounds on success probabilities for separable measurements

Constructed multipartite states demonstrating nonlocality in discrimination

Abstract

We consider multipartite quantum state discrimination and show that the minimum-error discrimination by separable measurements is closely related to the concept of entanglement witness. Based on the properties of entanglement witness, we establish some necessary and/or sufficient conditions on minimum-error discrimination by separable measurements. We also provide some conditions on the upper bound of the maximum success probability over all possible separable measurements. Our results are illustrated by examples of multidimensional multipartite quantum states. Finally, we provide a systematic way in terms of the entanglement witness to construct multipartite quantum state ensembles showing nonlocality in state discrimination.