Unambiguous Quantum State Discrimination in a PT$\mathcal {PT}$‐Symmetric System of a Single Trapped Ion

An unambiguous quantum state discrimination for two nonorthogonal states is demonstrated using a single ion. By implementing a non‐Hermitian Hamiltonian with parity‐time‐reversal (PT) symmetry, two candidate states evolve with different speed and become orthogonal at specific time, hence can be discriminated unambiguously. Experiments are performed for both the PT‐symmetry preserved and broken regimes, and the probabilities of successful discrimination, null measurement, and error are evaluated. Abstract An unambiguous quantum state discrimination of two qubit states is experimentally demonstrated under a non‐Hermitian Hamiltonian with parity‐time‐reversal (PT$\mathcal {PT}$) symmetry in a single trapped 40Ca+ ion. It is shown that any two non‐orthogonal states can become orthogonal subjected to time evolution of a PT$\mathcal {PT}$‐symmetric Hamiltonian in both the PT$\mathcal {PT}$‐symmetry preserving and broken regimes, thus can be discriminated unambiguously. For a given pair of candidate states, it is shown 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, a clear geometric picture and some analytic results are provided to understand the main conclusions. This work shows a promising application of non‐Hermitian physics in quantum information processing. An unambiguous quantum state discrimination for two nonorthogonal states is demonstrated using a single ion. By implementing a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry, two candidate states evolve with different speed and become orthogonal at specific time, hence can be discriminated unambiguously. Experiments are performed for both the PT-symmetry preserved and broken regimes, and the probabilities of successful discrimination, null measurement, and error are evaluated. Abstract An unambiguous quantum state discrimination of two qubit states is experimentally demonstrated under a non-Hermitian Hamiltonian with parity-time-reversal (PT$\mathcal {PT}$) symmetry in a single trapped 40 Ca + ion. It is shown that any two non-orthogonal states can become orthogonal subjected to time evolution of a PT$\mathcal {PT}$-symmetric Hamiltonian in both the PT$\mathcal {PT}$-symmetry preserving and broken regimes, thus can be discriminated unambiguously. For a given pair of candidate states, it is shown 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, a clear geometric picture and some analytic results are provided to understand the main conclusions. This work shows a promising application of non-Hermitian physics in quantum information processing. Advanced Science, Volume 12, Issue 42, November 13, 2025.