A detailed analysis of mathematics of entanglement in Non-Hermitian systems in real eigenvalue regime

TL;DR

This paper develops a formalism for analyzing entanglement in non-Hermitian quantum systems with real eigenvalues, extending density operator methods and entropy measures to these complex Hamiltonian models.

Contribution

It introduces a complete density operator formalism for non-Hermitian systems with real eigenvalues, including correct forms of Von-Neumann entropy and entanglement measures.

Findings

Formalism for density operators in non-Hermitian systems

Corrected forms of Von-Neumann entropy for these systems

Analysis of entanglement properties in the real eigenvalue regime

Abstract

Hamiltonian Mechanics works for conserved systems and Quantum Mechanics is given in Hamiltonian language. It is considered that complexifying the quantum Hamiltonian, a balanced loss and gain model can be created. The usual mathematics of density operator formalism and entanglement is extrapolated to such systems and the consequences are studied. Namely, a complete formalism using Density operators is created for real eigenvalue regime of these Non- Hermitian systems and correct forms of Von-Neumann and Entanglement Entropy are created. The consequences are studied in this regime and depicted w.r.t recent papers by [9, 20].