Linear quantum entropy and non-Hermitian Hamiltonians

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 partiallyWigner-transformed non-HermitianHamiltonian (which is typically usefulwithin amixed 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.