Single-shot discrimination of quantum unitary processes

TL;DR

This paper develops a framework for discriminating quantum processes, providing solutions for minimum-error and unambiguous discrimination, and introduces a fidelity-based bound that is saturated for unitary channels.

Contribution

It formulates quantum process discrimination problems using process POVMs and derives a fidelity-like bound, revealing that the same optimization applies to both discrimination tasks.

Findings

Solution for minimum-error discrimination of unitary channels

Fidelity-like lower bound on unambiguous discrimination failure probability

Optimal discrimination strategies are based on the same process fidelity measure

Abstract

We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a "fidelity-like" lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of apriori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimization of the same quantity called completely bounded process fidelity.