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

TL;DR

This paper experimentally demonstrates unambiguous quantum state discrimination using a $ ext{PT}$-symmetric Hamiltonian in a trapped ion system, enabling deterministic orthogonalization of non-orthogonal states and highlighting applications in quantum information processing.

Contribution

It provides the first experimental realization of quantum state discrimination under a $ ext{PT}$-symmetric Hamiltonian in a single trapped ion, including analysis of optimal parameters and geometric interpretation.

Findings

Non-orthogonal states can be made orthogonal via $ ext{PT}$-symmetric evolution.

Optimal Hamiltonian parameters exist for fastest state orthogonalization.

The method is applicable in both $ ext{PT}$-symmetric preserving and broken regimes.

Abstract

We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{PT}$) 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 $\mathcal{PT}$-symmetric Hamiltonian in both the $\mathcal{PT}$-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.