Optimal single shot strategies for discrimination of quantum measurements

TL;DR

This paper investigates the optimal strategies for discriminating quantum measurements with a single use, highlighting the advantages of ancilla-assisted methods and the role of entanglement in achieving perfect discrimination.

Contribution

It establishes necessary and sufficient conditions for perfect discrimination of binary measurements and analyzes the role of entanglement in discriminating multiple qubit measurements.

Findings

Ancilla-assisted schemes outperform simple schemes for perfect discrimination.

Discrimination of three qubit measurements requires bipartite entanglement.

Non-maximally entangled states can outperform maximally entangled states in certain scenarios.

Abstract

We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m <= n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific quantum states. In particular, the optimal protocol for discrimination of projective qubit measurements with fixed failure rate (exploiting maximally entangled test state) is described. While minimum error discrimination of two projective qubit measurements can be realized without any need of entanglement, we show that discrimination of three projective qubit measurements requires a bipartite probe state. Moreover, when the measurements are not projective, the non-maximally entangled test states can outperform the maximally entangled ones.