Paper
The effect of partial post-selection on quantum discrimination
Authors
Qipeng Qian, Christos N. Gagatsos
Abstract
The discrimination of quantum states is a central problem in quantum information science and technology. Meanwhile, partial post-selection has emerged as a valuable tool for quantum state engineering. In this work, we bring these two areas together and ask whether partial measurements can enhance the discrimination performance between two unknown and non-orthogonal pure states. Our framework is general: the two unknown states interact with the same environment-set in a pure state-via an arbitrary unitary transformation. A partial measurement is then performed on one of the output modes, modeled by an arbitrary positive operator-valued measure (POVM). We then allow classical communication to inform the unmeasured mode of the outcome of the partial measurement on the other mode, which is subsequently measured by a POVM that is optimal in the sense that the probability of error is minimized. The two POVMs act locally and classical information is exchanged between the two modes, representing a single-round (feed-forward) form of local operations with classical communication. Under these considerations, we first show that the minimum error probability, averaged over all possible post-selected branches, cannot be reduced below the minimum error probability of discriminating the original input states. Then, we identify using specific example that specific post-selection outcomes under which the conditional discrimination can achieve strictly lower error probabilities than the original optimal measurement, illustrating that while post-selection does not improve average performance, it can enable better discrimination in certain branches of the post-selected ensemble.