Tingting Shi

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.

Exceptional points featuring enhanced energy response to perturbation hold significant potential in detection and measurement of weak signals. Of particular interest is the existence and property of high-order exceptional points in quantum systems, owing to the capability to provide high-order response to perturbations. We investigate the exceptional points in a system of $n$ identical qubits possessing parity-time-reversal symmetry. We prove that owing to an incomplete coalescence of eigenstates, the highest possible order of exceptional point is $n+1$, which is also the upper bound of the order of energy response to perturbation. More interestingly, by considering an Ising-type interaction, we analytically prove that to achieve an $(m+1)$-th order response for any $m \le n$, the system must acquire a nontrivial $m$-body interaction. Finally, we propose a Floquet driving scheme to implement an effective multi-body Ising-type interaction, which can be realized in trapped ions or superconducting qubits.