| Quantum information science,which is formed by the fusion of quantum mechanics and information theory,is a frontier hot cross field.Non-Hermitian quantum systems are closely related to open systems and have many novel properties,which have potential value for the development of new theories,new experiments and new applications.Entropy is an important physical and informatics concept to describe the degree of disorder of the system or the uncertainty of information.The existing research is mainly for isolated systems or Hermitian quantum systems.This paper focuses on the theoretical research of information entropy of nonHermitian systems.We use von Neumann entropy to distinguish typical non-Hermitian quantum systems,and theoretically study the dynamic evolution characteristics of quantum states in eight typical non-Hermitian systems,including PT symmetric / antiPT symmetric,P pseudo-Hermitian symmetric / anti-P symmetric systems,and the corresponding systems are divided into two phase spaces by EP points.By calculating the evolution of von Neumann entropy with time in these systems,we find that the periodicity,asymptote and symmetry of information entropy dynamics in different systems are significantly different,and according to the characteristics of von Neumann entropy in different systems,a theoretical method for distinguishing the above nonHermitian systems is developed.In addition,we first propose the mathematical definition of non-Hermitian Rényi entropy,which is determined by both normalized and unnormalized density matrices in the evolution of quantum systems.The nonHermitian Rényi entropy proposed by us can directly calculate the information entropy of non-Hermitian systems,characterize the distribution of information entropy in nonHermitian systems and the flow of information entropy between the whole system and the external environment.Through the non-Hermitian two-level tunneling detuning model and its gauge transformation examples,we illustrate that the non-Hermitian Rényi entropy is more reasonable and advantageous in characterizing non-Hermitian systems.Our research has a promoting effect on characterizing the information entropy of non-Hermitian quantum systems. |
