Characterising memory in quantum channel discrimination via constrained separability problems

TL;DR

This paper investigates how limited quantum memory affects the ability to discriminate quantum channels, using separability constraints to analyze the problem and distinguish scenarios requiring quantum or classical memory.

Contribution

It introduces a novel framework using constrained separability problems to characterize memory effects in quantum channel discrimination.

Findings

Boundaries between quantum and classical memory requirements identified.

Method enables systematic analysis of adaptive channel discrimination protocols.

Insights into hierarchical relationships in memory-assisted discrimination protocols.

Abstract

Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.