Discriminating an Arbitrary Number of Pure Quantum States by the Combined $\mathcal{CPT}$ and Hermitian Measurements

TL;DR

This paper proposes a method combining $ ext{PT}$-symmetric and Hermitian measurements to discriminate an arbitrary number of pure quantum states, extending previous two-state discrimination techniques.

Contribution

It introduces a novel approach that allows the discrimination of multiple pure quantum states using combined $ ext{PT}$-symmetric and Hermitian measurements.

Findings

Discrimination of multiple pure states is achievable with appropriate $ ext{PT}$-symmetric Hamiltonian parameters.

The method extends two-state discrimination to multiple states.

The approach is theoretically feasible for arbitrary pure states.

Abstract

If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, $\mathcal{PT}$-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this approach by combining $\mathcal{PT}$-symmetric and Hermitian measurements and show that it's possible to distinguish an arbitrary number of pure quantum states by an appropriate choice of the parameters of $\mathcal{PT}$-symmetric Hamiltonian.