Minimum-Consumption Discrimination of Quantum States via Globally Optimal Adaptive Measurements

Reducing the average resource consumption is the central quest in discriminating non -orthogonal quantum states for a fixed admissible error rate epsilon. The globally optimal fixed local projective measurement for this task is found to be different from that for previous minimum -error discrimination tasks [S. Slussarenko et al., Phys. Rev. Lett. 118, 030502 (2017)]. To achieve the ultimate minimum average consumption, here we develop a general globally optimal adaptive strategy (GOA) by subtly using the updated posterior probability, which works under any error rate requirements and any one-way measurement restrictions, and can be solved by a convergent iterative relation. First, under the local measurement restrictions, our GOA is solved to serve as the local bound, which saves 16.6 copies (24%) compared with the previously best globally optimal fixed local projective measurement. When the more powerful two -copy collective measurements are allowed, our GOA is experimentally demonstrated to beat the local bound by 3.9 copies (6.0%). By exploiting both adaptivity and collective measurements, our Letter marks an important step toward minimum -consumption quantum state discrimination.