On the Chernoff distance for asymptotic LOCC discrimination of bipartite quantum states

TL;DR

This paper explores the limits of local operations and classical communication (LOCC) in distinguishing bipartite quantum states, revealing that for certain data hiding states, the optimal measurement strategy remains unchanged even with many copies.

Contribution

It determines the optimal error probability and measurement strategy for many copies of data hiding states using linear programming, showing single-copy measurements remain optimal.

Findings

Single-copy optimal measurement remains optimal for multiple copies.

Established a lower bound on distinguishability bias with separable operations.

Provided a linear programming approach to optimal discrimination of data hiding states.

Abstract

Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication (LOCC), in the limit of many copies. While for two pure states a result of Walgate et al. shows that LOCC is just as powerful as global measurements, data hiding states (DiVincenzo et al.) show that locality can impose severe restrictions on the distinguishability of even orthogonal states. Here we determine the optimal error probability and measurement to discriminate many copies of particular data hiding states (extremal d x d Werner states) by a linear programming approach. Surprisingly, the single-copy optimal measurement remains optimal for n copies, in the sense that the best strategy is measuring each copy separately, followed by a simple classical decision rule. We also put a lower bound on the bias with which states can be distinguished by separable operations.