Memory Effects in Quantum State Verification


We consider the quantum memory assisted state verification task, where the local verifiers can store copies of quantum states and measure them collectively. We establish an exact analytic formula for optimizing two-copy state verification and give a globally optimal two-copy strategy for multi-qubit graph states involving only Bell measurements. For arbitrary memory availability, we present a dimension expansion technique that designs efficient verification strategies, showcasing its application to GHZ-like states. These strategies become increasingly advantageous with growing memory resources, ultimately approaching the theoretical limit of efficiency. Our findings demonstrate that quantum memories dramatically enhance state verification efficiency, sheding light on error-resistant strategies and practical applications of large-scale quantum memory-assisted verification.

arXiv preprint arXiv:2312.11066