Limitations on separable measurements by convex optimization

TL;DR

This paper establishes fundamental limitations on local operations and classical communication (LOCC) and separable measurements in bipartite quantum state discrimination, providing exact formulas, characterizations, and bounds using convex optimization techniques.

Contribution

It introduces new analytical tools and results that precisely quantify the capabilities and limitations of separable measurements in quantum state discrimination.

Findings

Exact formula for discriminating Bell states with ancillary entanglement

Characterization of when unextendable product sets are perfectly discriminated by separable measurements

Optimal success probability bounds for specific bipartite state discrimination problems

Abstract

We prove limitations on LOCC and separable measurements in bipartite state discrimination problems using techniques from convex optimization. Specific results that we prove include: an exact formula for the optimal probability of correctly discriminating any set of either three or four Bell states via LOCC or separable measurements when the parties are given an ancillary partially entangled pair of qubits; an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements, along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements; and an optimal bound on the success probability for any LOCC or separable measurement for the recently proposed state discrimination problem of Yu, Duan, and Ying.