Quantum state discrimination in a $\mathcal{P}\mathcal{T}$-symmetric system of a single trapped ion

Abstract

We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{P}\mathcal{T}$) symmetry in a single trapped ${}^{40}$Ca${}^{+}$ ion. We show that any two non-orthogonal states can become orthogonal subjected to time evolution of a $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian in both the $\mathcal{P}\mathcal{T}$-symmetry preserving and broken regimes, thus can be discriminated deterministically. For a given pair of candidate states, we show that the parameters of the Hamiltonian must be confined in a proper range, within which there exists an optimal choice to realize quantum brachistochrone for the fastest orthogonalization. Besides, we provide a clear geometric picture and some analytic results to understand the main conclusions. Our work shows a promising application of non-Hermitian physics in quantum information processing.

arXiv comment6 pages, 4 figures