Quantum state discrimination in a PT-symmetric system

TL;DR

This paper experimentally demonstrates quantum state discrimination in a PT-symmetric non-Hermitian system, showing rapid evolution into orthogonal states and comparing its efficiency to Hermitian systems, with implications for quantum information processing.

Contribution

The study introduces the concept of PT-symmetric quantum state discrimination and experimentally explores its properties and advantages over traditional Hermitian approaches.

Findings

Nonorthogonal states can rapidly become orthogonal under PT-symmetric evolution.

Discrimination cost involves dissipation into the environment.

At critical parameters, PT-symmetric QSD matches optimal Hermitian unambiguous discrimination.

Abstract

Nonorthogonal quantum state discrimination (QSD) plays an important role in quantum information and quantum communication. In addition, compared to Hermitian quantum systems, parity-time-($\mathcal{PT}$-)symmetric non-Hermitian quantum systems exhibit novel phenomena and have attracted considerable attention. Here, we experimentally demonstrate QSD in a $\mathcal{PT}$-symmetric system (i.e., $\mathcal{PT}$-symmetric QSD), by having quantum states evolve under a $\mathcal{PT}$-symmetric Hamiltonian in a lossy linear optical setup. We observe that two initially nonorthogonal states can rapidly evolve into orthogonal states, and the required evolution time can even be vanishing provided the matrix elements of the Hamiltonian become sufficiently large. We also observe that the cost of such a discrimination is a dissipation of quantum states into the environment. Furthermore, by comparing $\mathcal{PT}$-symmetric QSD with optimal strategies in Hermitian systems, we find that at the critical value, $\mathcal{PT}$-symmetric QSD is equivalent to the optimal unambiguous state discrimination in Hermitian systems. We also extend the $\mathcal{PT}$-symmetric QSD to the case of discriminating three nonorthogonal states. The QSD in a $\mathcal{PT}$-symmetric system opens a new door for quantum state discrimination, which has important applications in quantum computing, quantum cryptography, and quantum communication.