Entanglement cost of discriminating noisy Bell states by local operations and classical communication

TL;DR

This paper investigates the minimum entanglement needed for optimal local discrimination of noisy Bell states, revealing that a Bell state is essential even when the ensemble lacks maximally entangled states.

Contribution

It proves that Bell states are necessary for optimal LOCC discrimination of noisy Bell ensembles, regardless of the entanglement in the ensemble.

Findings

Bell states are required for optimal discrimination by LOCC.

No maximally entangled state is necessary in the ensemble.

Entanglement cost remains high even with noisy states.

Abstract

Entangled states can help in quantum state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper, we consider the task of LOCC discrimination of the states of noisy Bell ensembles, where a given ensemble consists of the states obtained by mixing the Bell states with an arbitrary two-qubit state with nonzero probabilities. It is proved that a Bell state is required for optimal discrimination by LOCC, even though the ensembles do not contain, in general, any maximally entangled state, and in specific instances, any entangled state.