Local discrimination of mixed states

TL;DR

This paper establishes tight bounds on the error probability for local discrimination of mixed qubit states, showing LOCC protocols are less efficient than collective ones, especially asymptotically.

Contribution

It provides the first rigorous, efficiently computable bounds on LOCC discrimination error rates for mixed states, highlighting fundamental limitations compared to collective measurements.

Findings

LOCC performs strictly worse than collective measurements for mixed states.

The gap between LOCC and collective error rates persists asymptotically.

LOCC requires up to twice the number of copies to match collective measurement accuracy.

Abstract

We provide rigorous, efficiently computable and tight bounds on the average error probability of multiple-copy discrimination between qubit mixed states by Local Operations assisted with Classical Communication (LOCC). In contrast to the pure-state case, these experimentally feasible protocols perform strictly worse than the general collective ones. Our numerical results indicate that the gap between LOCC and collective error rates persists in the asymptotic limit. In order for LOCC and collective protocols to achieve the same accuracy, the former requires up to twice the number of copies of the latter. Our techniques can be used to bound the power of LOCC strategies in other similar settings, which is still one of the most elusive questions in quantum communication.