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arXiv · 2502.20717

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

Chenhao Zhu·Tingting Shi·Liangyu Ding·Zhiyue Zheng·Xiang Zhang·Wei Zhang
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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.

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Chenhao Zhu, Tingting Shi, Liangyu Ding, Zhiyue Zheng, Xiang Zhang, Wei Zhang. 2025-02-28. Quantum state discrimination in a $\mathcal{PT}$-symmetric system of a single trapped ion. https://arxiv.org/abs/2502.20717

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