A framework for bounding nonlocality of state discrimination

TL;DR

This paper introduces a framework to quantify the nonlocality of bipartite quantum states in state discrimination tasks, providing bounds on LOCC protocol performance and resolving open questions about specific state bases.

Contribution

It offers a new method to bound nonlocality in quantum state discrimination, simplifying proofs and extending results to larger dimensions and rotated bases.

Findings

Bound on nonlocality in bipartite state discrimination

Simplified proof for domino states nonlocality

Extension to larger dimensions and rotated bases

Abstract

We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99].