Optimal success probability for arbitrary measurement discrimination

Characterize the optimal success probability for discriminating arbitrary sets of quantum measurements, thereby quantitatively comparing global, restricted LOCC, and adaptive LOCC discrimination strategies in analogy with quantitative results for quantum-state discrimination.

Background

The paper establishes qualitative separations between global discrimination, restricted local strategies, and adaptive LOCC strategies for product measurements. In particular, some measurement sets are globally distinguishable but locally indistinguishable, while adaptive protocols can outperform restricted protocols.

The authors identify the absence of a general quantitative theory of these separations. Determining the optimal success probability for arbitrary measurement sets would quantify the operational gap between the different discrimination paradigms, extending the paper’s perfect-discrimination results.

References

Several directions remain open. A natural next step is to characterize the optimal success probability for discriminating arbitrary measurement sets, yielding a quantitative characterization of the gap between discrimination paradigms, analogous to that for quantum states.

— Nonlocality without entanglement for multipartite quantum measurements  (2610.02032 - Manna et al., 1 Oct 2026) in Section Discussion

A direction for future work is to explore multishot nonlocality without entanglement, where multiple uses of the unknown measurement are available, and to determine whether local indistinguishability persists or can be activated by collective probing across multiple uses.

— Nonlocality without entanglement for multipartite quantum measurements  (2610.02032 - Manna et al., 1 Oct 2026) in Section Discussion