If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, it is not possible to discriminate them by a single measurement due to the unitarity constraint. In a regular Hermitian quantum mechanics, the successful discrimination is possible to perform with the probability $p < 1$, while in $\mathcal{PT}$-symmetric quantum mechanics a \textit{simulated single-measurement} quantum state discrimination with the success rate $p$ can be done. We extend the $\mathcal{PT}$-symmetric quantum state discrimination approach for the case of three pure quantum states, $|\psi_1\rangle$, $|\psi_2\rangle$ and $|\psi_3\rangle$ without any additional restrictions on the geometry and symmetry possession of these states. We discuss the relation of our approach with the recent implementation of $\mathcal{PT}$ symmetry on the IBM quantum processor.
翻译：如果已知这个系统位于两个非垂直量度状态之一,即$ ⁇ psi_1\rangle$或$ ⁇ psi_2\rcangle$,那么由于单一性限制,不可能通过单一度量来区别对待它们。在普通的赫米特里量量量力力力力学中,有可能以概率 < 1美元进行成功的区分,而在$\mathcal{PT} $-对称量量量力力力力力学中,则可以做到一种\ textit{simulate 单度量量量力学} 量量量量力学歧视,而成功率为$\mathcal{PT} 美元。我们在IBM 量量量力处理器中对三种纯量量力学状态,即$ ⁇ si_1\\\\rangle$、$ ⁇ psi_2\rangle$和$ ⁇ psi_3\rangle$的情况下,我们的方法与最近实施的 $\mathcal{TP}对调之间的关系。我们讨论了我们的方法与最近实施IBM 量量力过程的关联。
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