$\mathcal{PT}$-Symmetric Quantum Discrimination of Three States

• URL: http://arxiv.org/abs/2012.14897v2
• Date: Sun, 6 Jun 2021 18:52:43 GMT
• Title: $\mathcal{PT}$-Symmetric Quantum Discrimination of Three States
• Authors: Yaroslav Balytskyi, Manohar Raavi, Anatoliy Pinchuk and Sang-Yoon Chang
• Abstract summary: In a regular Hermitian quantum mechanics, the successful discrimination is possible with the probability $p 1$. In $mathcalPT$-symmetric quantum mechanics a textitsimulated single-measurement quantum state discrimination with the success rate $p$ can be done. We discuss the relation of our approach with the recent implementation of $mathcalPT$ symmetry on the IBM quantum processor.
• Score: 2.011085769303415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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