Unambiguous Quantum State Discrimination in a PTPT‐Symmetric System of a Single Trapped Ion

An unambiguous quantum state discrimination of two qubit states is experimentally demonstrated under a non‐Hermitian Hamiltonian with parity‐time‐reversal () 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 ‐symmetric Hamiltonian in both the ‐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.