Distinguish between typical non-Hermitian quantum systems by entropy dynamics

Daili Li,Chao Zheng

doi:10.1038/s41598-022-06808-1

Abstract

Non-Hermitian (NH) quantum systems attract research interest increasingly in recent years, among which the PT-symmetric, P-pseudo-Hermitian and their anti-symmetric counterpart systems are focused much more. In this work, we extend the usage of entropy to distinguish time-evolutions of different classes and phases of typical NH-systems. In detail, we investigate the entropy dynamics of two-level NH-systems after quantum decoherence induced by single-qubit projective measurements, finding that it depends on both the initial states and the selection of the computational bases of the measurements. In a general case, we show how to distinguish all the eight phases of the above NH-systems step by step, in which process three different initial states are necessary if the basis of measurement is fixed. We propose how the distinguishing process is realized in quantum simulation, in which quantum tomography is not needed. Our investigations can be applied to judge phase transitions of non-Hermitian systems.

Highlights

Non-Hermitian (NH) quantum systems attract research interest increasingly in recent years, among which the PT-symmetric, P-pseudo-Hermitian and their anti-symmetric counterpart systems are focused much more
The exact PT and PT-broken phases exist in an anti-PT-symmetric system, and the phase transition occurs at the exceptional points (EPs), leading to many counter-intuitive phenomena
We extend the usage of the entropy dynamics to distinguish different phases of the four classes of non-Hermitian Hamiltonians, i.e., Department of Physics, College of Science, North China University of Technology, Beijing 100144, People’s Republic of China. *email: czheng@ncut.edu.cn

Summary

Introduction

Non-Hermitian (NH) quantum systems attract research interest increasingly in recent years, among which the PT-symmetric, P-pseudo-Hermitian and their anti-symmetric counterpart systems are focused much more. We will describe the two-dimensional NH-systems in detail, which can be treat as the mathematical preparations and theoretical models to distinguish between them by their entropy dynamics after time evolutions and measurement-induced quantum decoherences.

Results

Conclusion