Generalized quantum process discrimination problems

TL;DR

This paper develops a comprehensive framework for quantum process discrimination, encompassing various strategies and complexities, providing convex formulations, duality results, symmetry considerations, and practical examples including single-shot channel discrimination.

Contribution

It introduces a unified convex approach to quantum process discrimination, deriving duality and symmetry results, and providing analytical solutions for specific cases.

Findings

Convex formulation with no duality gap for process discrimination

Existence of symmetric optimal solutions under certain conditions

Analytical solution for a single-shot channel discrimination problem

Abstract

We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have an internal memory. Given a collection of candidate processes, our task is to find a discrimination strategy, which may be adaptive and/or entanglement-assisted, that maximizes a given objective function subject to given constraints. Our problem can be formulated as a convex problem. Its Lagrange dual problem with no duality gap and necessary and sufficient conditions for an optimal solution are derived. We also show that if a problem has a certain symmetry and at least one optimal solution exists, then there also exists an optimal solution with the same type of symmetry. A minimax strategy for a process discrimination problem is also discussed. As applications of our results, we provide some problems in which an adaptive strategy is not necessary for optimal discrimination. We also present an example of single-shot channel discrimination for which an analytical solution can be obtained.