Minimum error discrimination of Pauli channels

Abstract

We solve the problem of discriminating with minimum error probability two given Pauli channels. We show that, unlike in the case of discrimination between unitary transformations, the use of entanglement with an ancillary system can strictly improve the discrimination, and any maximally entangled state allows one to achieve the optimal discrimination. We also provide a simple necessary and sufficient condition in terms of the structure of the channels for which the ultimate minimum error probability can be achieved without entanglement assistance. When such a condition is satisfied, the optimal input state is simply an eigenstate of one of the Pauli matrices.