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

Abstract

The theory of a two-level $\hat{I}\cdot$-Hermitian Hamiltonian with $\mathcal{P}\mathcal{T}$ 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 $\mathcal{P}\mathcal{T}-$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 $\mathcal{P}\mathcal{T}-$symmetric Hamiltonian, and the results are compared with their corresponding two-level Hermitian counterparts. The nature of entanglement between two $\mathcal{P}\mathcal{T}-$symmetric and Hermitian open quantum systems is calculated, and the contrast observed.

14 pages, 6 figures