  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.
