Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states ${ rho_{j} }$ while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible. In this work, we focus on using RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally introduce a min-entropy based locally adaptive protocol, and demonstrate that the RLNN strategy meets or exceeds the min-entropy success probability in each random trial. While the use of RLNN is highly successful for designing adaptive local measurement strategies, we find that there can be a significant gap between success probability of any locally-adaptive measurement strategy and the optimal collective measurement. As evidence of this, we exhibit a collection of pure tensor product quantum states which cannot be optimally distinguished by any locally-adaptive strategy. This counterexample raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.
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