Discriminating an Arbitrary Number of Pure Quantum States by the Combined $\mathcal{CPT}$ and Hermitian Measurements
This work addresses a fundamental challenge in quantum information processing for physicists and engineers, representing an incremental extension of existing methods.
The paper tackles the problem of discriminating an arbitrary number of pure quantum states by extending a previous approach that used PT-symmetric quantum mechanics for two states, showing that combining PT-symmetric and Hermitian measurements enables this discrimination through parameter choice in the Hamiltonian.
If the system is known to be in one of two non-orthogonal quantum states, $|ψ_1\rangle$ or $|ψ_2\rangle$, $\mathcal{PT}$-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.