Quantum process discrimination with restricted strategies

TL;DR

This paper develops a convex optimization framework for quantum process discrimination under strategy restrictions, providing conditions for optimality and linking performance to robustness measures, thus advancing understanding of restricted quantum discrimination.

Contribution

It introduces a general convex optimization approach with zero duality gap for restricted quantum process discrimination, applicable to any strategy subset, and relates performance to robustness measures.

Findings

Dual problem often easier to solve than the primal

Optimal performance characterized by robustness measures

Framework applicable to various restricted strategies

Abstract

The discrimination of quantum processes, including quantum states, channels, and superchannels, is a fundamental topic in quantum information theory. It is often of interest to analyze the optimal performance that can be achieved when discrimination strategies are restricted to a given subset of all strategies allowed by quantum mechanics. In this paper, we present a general formulation of the task of finding the maximum success probability for discriminating quantum processes as a convex optimization problem whose Lagrange dual problem exhibits zero duality gap. The proposed formulation can be applied to any restricted strategy. We also derive necessary and sufficient conditions for an optimal restricted strategy to be optimal within the set of all strategies. We provide a simple example in which the dual problem given by our formulation can be much easier to solve than the original problem. We also show that the optimal performance of each restricted process discrimination problem can be written in terms of a certain robustness measure. This finding has the potential to provide a deeper insight into the discrimination performance of various restricted strategies.