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

Abstract

If the system is known to be in one of two non-orthogonal quantum states, $|{\psi }_1⟩$ or $|{\psi }_2⟩$, $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this approach by combining $\mathcal{P}\mathcal{T}$-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 $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian.