Entanglement-breaking channels are a quantum memory resource

TL;DR

This paper demonstrates that entanglement-breaking channels, despite destroying quantum correlations, still serve as a quantum memory resource in multi-time scenarios, outperforming classical memories of the same size.

Contribution

It reveals that entanglement-breaking channels cannot be considered purely classical in temporal quantum memory tasks, providing explicit examples of their quantum advantage.

Findings

Entanglement-breaking channels outperform classical memories in certain tasks.

They cannot be simulated by classical systems of the same dimension.

They challenge the notion of these channels as purely classical resources.

Abstract

Entanglement-breaking channels (equivalently, measure-and-prepare channels) are an important class of quantum operations noted for their ability to destroy multipartite spatial quantum correlations. Inspired by this property, they have also been employed in defining notions of "classical memory", under the assumption that such channels effectively act as a classical resource. We show that, in a single-system multi-time scenario, entanglement-breaking channels are still a quantum memory resource: a qudit going through an entanglement-breaking channel cannot be simulated by a classical system of same dimension. We provide explicit examples of memory-based output generation tasks where entanglement-breaking channels outperform classical memories of the same size. Our results imply that entanglement-breaking channels cannot be generally employed to characterize classical memory effects in temporal scenarios without additional assumptions.