Abstract
We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly considered.
Highlights
The study of open quantum systems is one of the fundamental problems of modern physics [1,2].An open quantum system consists of a region of space where quantum processes take place in contact with a decohering and dissipative environment that is typically beyond the control of the experimenter
We have shown that it is possible to define meaningful entropy functionals for open quantum systems described by non-Hermitian Hamiltonians
A non-Hermitian generalisation of the von Neumann entropy, which is able to signal the loss of information of the quantum subsystem, requires both the normalised and the non-normalised density matrix: this entropy can be defined as the normalised average of the logarithm of the non-normalised density matrix [25]
Summary
The study of open quantum systems is one of the fundamental problems of modern physics [1,2]. Since the (partial) Wigner representation is useful in order to derive a mixed quantum-classical description of non-Hermitian systems [27], it becomes interesting to study the properties of the so-called linear entropy [26,28,29] and its generalisation to the case of open quantum systems described by general non-Hermitian Hamiltonians. To this end, we present in this paper, for the first time to our knowledge, a generalisation of the entropy for systems with non-Hermitian Hamiltonians that must be adopted when there is an embedding of the quantum subsystem in phase space.
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