Characterizing Acceptance in Post-Selection One-Shot Quantum Hypothesis Testing

In post-selection hypothesis testing, a third outcome is added, corresponding to not selecting any of the hypotheses. In this paradigm, minimum error for various cases is characterized in literature conditioned on the fact that one of the selected outcomes occurs. However, not selecting any of the hypotheses decimates the quality of testing. There is no discussion on the quality of post-selection hypothesis testing. In this work, we characterize the quality of post-selection hypothesis testing by defining a new metric acceptance. We find out measurements which lead to optimal post-selection error. For these measurements, we have derived the expression for acceptance in post-selection symmetric and asymmetric hypothesis testing problems. We have also given closed-form expressions in some specific cases.