Robustness of Quantum Memories: An Operational Resource-Theoretic Approach

Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for any quantum technology to exhibit operational advantage. There is thus great value in identifying physically meaningful means to benchmark candidate quantum memories against each other across diverse operational settings. Here we introduce the robustness of quantum memory, and prove that it satisfies all the mathematical properties we expect of a bona-fide resource-theoretic measure of a system's capacity to retain non-classical information. We demonstrate its operational meaning as a resource in three different settings: (1) the resource cost of synthesising the memory with idealised qubit memories, (2) the resource cost of simulating the memory's observational statistics with classical resources, and (3) the performance of the memory in discriminating different input states. We illustrate an efficient semi-definite program to estimate the robustness of quantum memory, and show that it can be lower bounded with a single witness or purity measurement. Our results thus provide an experimentally accessible and operationally meaningful quantifier of the resources behind preserving quantum information.