Optimal discrimination between quantum operations

TL;DR

This paper presents exact methods for discriminating between two quantum operations, especially single qubit and Pauli channels, using unentangled states and provides conditions for perfect discrimination based on channel properties.

Contribution

It introduces an exact minimum error probability for single qubit quantum operations and characterizes conditions for perfect discrimination of generalized Pauli channels.

Findings

Exact minimum error probability for single qubit operations

Orthogonality condition for perfect discrimination of Pauli channels

Visual approach for Pauli channel discrimination

Abstract

In this paper, we address the problem of discriminating two given quantum operations. Firstly, based on the Bloch representation of single qubit systems, we give the exact minimum error probability of discriminating two single qubit quantum operations by unentangled input states. In particular, for the Pauli channels discussed in [Phys. Rev. A {\bf 71}, 062340 (2005)], we use a more intuitional and visual method to deal with their discrimination problem. Secondly, we consider the condition for perfect discrimination of two quantum operations. Specially, we get that two generalized Pauli channels are perfectly distinguishable if and only if their characteristic vectors are orthogonal.