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

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.