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

Paper link: https://advanced.onlinelibrary.wiley.com/doi/10.1002/advs.202510384