If the system is known to be in one of two non-orthogonal quantum states, ∣ψ1⟩ or ∣ψ2⟩, 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 PT-symmetric quantum mechanics a \textit{simulated single-measurement} quantum state discrimination with the success rate p can be done. We extend the PT-symmetric quantum state discrimination approach for the case of three pure quantum states, ∣ψ1⟩, ∣ψ2⟩ and ∣ψ3⟩ 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 PT symmetry on the IBM quantum processor.
@article{arxiv.2012.14897,
title = {$\mathcal{PT}$-Symmetric Quantum Discrimination of Three States},
author = {Yaroslav Balytskyi and Manohar Raavi and Anatoliy Pinchuk and Sang-Yoon Chang},
journal= {arXiv preprint arXiv:2012.14897},
year = {2021}
}