$\mathcal{PT}$-Symmetric Quantum Discrimination of Three States
This work addresses a fundamental limitation in quantum information processing for discriminating multiple quantum states, though it appears incremental as it extends an existing approach from two to three states.
The paper tackles the problem of discriminating among three non-orthogonal quantum states using a single measurement, extending a PT-symmetric quantum mechanics approach from two to three states without geometric or symmetry restrictions, achieving a success rate p as in the two-state case. It relates this method to recent implementations on IBM quantum processors.
If the system is known to be in one of two non-orthogonal quantum states, $|ψ_1\rangle$ or $|ψ_2\rangle$, 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, $|ψ_1\rangle$, $|ψ_2\rangle$ and $|ψ_3\rangle$ 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.