If the system is known to be in one of two non-orthogonal quantum states,
$|psi_1rangle$ or $|psi_2rangle$, 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,
$|psi_1rangle$, $|psi_2rangle$ and $|psi_3rangle$ 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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