Linear Quantum Entropy and Non-Hermitian Hamiltonians

TL;DR

This paper explores how to define quantum linear entropy for open quantum systems described by non-Hermitian Hamiltonians, addressing information flow in mixed quantum-classical dynamics.

Contribution

It introduces novel definitions of quantum linear entropy applicable to non-Hermitian Hamiltonian systems, including mixed quantum-classical representations.

Findings

Proposes new linear entropy functionals for non-Hermitian systems

Analyzes pure non-Hermitian Hamiltonian dynamics

Considers non-Hermitian dynamics in classical baths

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.