Capability of local operations and classical communication for distinguishing bipartite unitary operations

TL;DR

This paper investigates when local operations and classical communication (LOCC) are sufficient to optimally distinguish bipartite unitary operations, showing LOCC can match global performance for certain two-qubit unitaries with a single query.

Contribution

The paper demonstrates that for two-qubit entangling unitaries, LOCC can achieve optimal distinguishability matching global operations when only one query is used.

Findings

LOCC matches global distinguishability for certain two-qubit unitaries

Perfect distinguishability by global implies perfect by LOCC

LOCC achieves optimal discrimination probability when global cannot

Abstract

The problem behind this paper is, if the number of queries to unitary operations is fixed, say $k$, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We consider the above problem for two-qubit unitary operations in the case of $k=1$, showing that for two two-qubit entangling unitary operations without local parties, LOCC achieves the same distinguishability as the global operations. Specifically, we obtain: (i) if such two unitary operations are perfectly distinguishable by global operations, then they are perfectly distinguishable by LOCC too, and (ii) if they are not perfectly distinguishable by global operations, then LOCC can achieve the same optimal discrimination probability as the global operations.