The Perfect Distinguishability of Quantum Operations

TL;DR

This paper establishes a complete criterion for perfectly distinguishing unknown quantum operations with finite queries and introduces an optimal protocol, revealing that no auxiliary systems are needed for certain cases.

Contribution

It provides a necessary and sufficient condition for perfect distinguishability of quantum operations and designs an optimal discrimination protocol.

Findings

A complete characterization of perfect distinguishability conditions.

An optimal protocol for discriminating two quantum operations with minimal queries.

Perfect discrimination between two isometries without auxiliary systems or entanglement.

Abstract

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretely selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, employing the techniques from the theory of $q$-numerical range we find that an optimal perfect discrimination between two isometries is always achievable without using auxiliary systems or entanglement.