Minimum-consumption discrimination of quantum states via globally optimal adaptive measurements

Abstract

Reducing the average resource consumption is the central quest in discriminating non-orthogonal quantum states for a fixed admissible error rate $\varepsilon$. The globally optimal fixed local projective measurement (GOFL) for this task is found to be different from that for previous minimum-error discrimination tasks [PRL 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 requirement 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 GOFL. 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 work marks an important step towards minimum-consumption quantum state discrimination.