Quantum memory assisted entangled state verification with local measurements

Abstract: We consider the quantum memory assisted quantum state verification task, where an adversary prepare independent multipartite entangled states and send to the local verifiers, who then store several copies in the quantum memory and measure them collectively to make decision. We establish an exact analytic formula for optimizing two-copy state verification, where the verifiers store two copies, and give a globally optimal two-copy strategy for multi-qubit graph states involving only Bell measurements. When the verifiers can store arbitrarily many copies, we present a dimension expansion technique that designs efficient verification strategies for this case, showcasing its application to efficiently verifying 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 enhance state verification efficiency, sheding light on error-resistant strategies and practical applications of large-scale quantum memory-assisted verification.