Bipartite quantum state discrimination and decomposable entanglement witness

TL;DR

This paper explores how bipartite quantum state discrimination with positive-partial-transpose measurements relates to entanglement witnesses, establishing conditions and bounds for optimal discrimination using decomposable entanglement witnesses.

Contribution

It introduces a novel connection between minimum-error discrimination and decomposable entanglement witnesses, providing conditions and bounds for positive-partial-transpose measurement success.

Findings

Established conditions for minimum-error discrimination using PPT measurements

Derived upper bounds on maximum success probability for PPT measurements

Illustrated results with examples of multidimensional bipartite states

Abstract

We consider bipartite quantum state discrimination using positive-partial-transpose measurements and show that minimum-error discrimination by positive-partial-transpose measurements is closely related to entanglement witness. By using the concept of decomposable entanglement witness, we establish conditions on minimum-error discrimination by positive-partial-transpose measurements. We also provide conditions on the upper bound of the maximum success probability over all possible positive-partial-transpose measurements. Finally, we illustrate our results using examples of multidimensional bipartite quantum states.