In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added, corresponding to not selecting any of the hypotheses. In postselected scenario, minimum error one-shot symmetric hypothesis testing is characterized in literature conditioned on the fact that one of the selected outcomes occur. We proceed further in this direction to give the set of all possible measurements that lead to the minimum error. We have given an arbitrary error-minimizing measurement in a parametric form. Note that not selecting any of the hypotheses decimates the quality of testing. We further give an example to show that these measurements vary in quality. There is a need to discuss the quality of postselected hypothesis testing. We then characterize the quality of postselected hypothesis testing by defining a new metric acceptance and give expression of acceptance for an arbitrary error-minimizing measurement in terms of some parameters of the measurement. On the set of measurements that achieve minimum error, we have maximized the acceptance, and given an example which achieves that, thus giving an example of the best possible measurement in terms of acceptance.

翻译：在量子态假设检验中，给定一个包含两种可能状态之一的黑盒，通过执行测量以支持其中一个假设。在后选择假设检验中，会引入第三个结果，对应于不选择任何假设。文献中已对后选择场景下单次对称假设检验的最小误差问题进行了描述，其条件为所选结果之一必须发生。我们沿此方向进一步推进，给出了所有能够实现最小误差的可能测量集合。我们以参数化形式给出了任意误差最小化测量。需注意，不选择任何假设会降低检验质量。我们进一步通过示例说明这些测量在质量上存在差异。因此有必要讨论后选择假设检验的质量问题。随后，我们通过定义一个新度量——接受率——来刻画后选择假设检验的质量，并以测量参数的函数形式给出了任意误差最小化测量的接受率表达式。在实现最小误差的测量集合上，我们最大化接受率，并给出了达到该最大值的实例，从而在接收率意义上提供了最优测量的范例。