$\mathcal{PT-}$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets

TL;DR

This paper extends the theory of $ ext{PT}$-symmetric two-level quantum systems to open dynamics, deriving a master equation and analyzing information theoretic measures and entanglement properties.

Contribution

It provides a first-principles derivation of a $ ext{PT}$-symmetric master equation and compares information theoretic and entanglement features with Hermitian systems.

Findings

Non-Markovian witness and fidelity differ between $ ext{PT}$-symmetric and Hermitian systems.

Entanglement behavior shows contrast between $ ext{PT}$-symmetric and Hermitian cases.

Abstract

The theory of a two-level $\eta$-Hermitian Hamiltonian with $\mathcal{PT}$ symmetry is reviewed and extended to include open system dynamics. A first-principles derivation of the generalized Gorini-Kossakowski-Sudarshan-Lindblad master equation appropriate for a $\mathcal{PT}-$symmetric Hamiltonian is presented. Inspired by a simple light matter interaction open system model, information theoretic quantities like a non-Markovian witness and fidelity are calculated for the $\mathcal{PT-}$symmetric Hamiltonian, and the results are compared with their corresponding two-level Hermitian counterparts. The nature of entanglement between two $\mathcal{PT-}$symmetric and Hermitian open quantum systems is calculated, and the contrast observed.