A resource theory of quantum memories and their faithful verification with minimal assumptions

TL;DR

This paper develops a resource theory framework for quantum memories, providing complete, faithful, and experimentally feasible tests to verify genuine quantum storage capabilities with minimal assumptions.

Contribution

It introduces a resource theory of quantum memories, establishing complete game-theoretic conditions for certification that are faithful and require only trusted inputs.

Findings

Complete set of conditions for quantum memory certification

Tests are faithful and can certify non-entanglement-breaking channels

Experimental feasibility demonstrated even with high losses

Abstract

We provide a complete set of game-theoretic conditions equivalent to the existence of a transformation from one quantum channel into another one, by means of classically correlated pre/post processing maps only. Such conditions naturally induce tests to certify that a quantum memory is capable of storing quantum information, as opposed to memories that can be simulated by measurement and state preparation (corresponding to entanglement-breaking channels). These results are formulated as a resource theory of genuine quantum memories (correlated in time), mirroring the resource theory of entanglement in quantum states (correlated spatially). As the set of conditions is complete, the corresponding tests are faithful, in the sense that any non entanglement-breaking channel can be certified. Moreover, they only require the assumption of trusted inputs, known to be unavoidable for quantum channel verification. As such, the tests we propose are intrinsically different from the usual process tomography, for which the probes of both the input and the output of the channel must be trusted. An explicit construction is provided and shown to be experimentally realizable, even in the presence of arbitrarily strong losses in the memory or detectors.