Entanglement of pseudo-Hermitian random states

TL;DR

This paper explores the entanglement properties of pseudo-Hermitian random states, revealing that their entanglement differs from Fock states and is more akin to Bell states, extending previous work on PT-symmetric systems.

Contribution

It recasts previous results on PT-symmetric systems into a pseudo-Hermitian random matrix framework, highlighting the nature of entanglement in Bell states rather than Fock states.

Findings

Entanglement in pseudo-Hermitian states differs from Fock states.

Formalism aligns with previous PT-symmetric results.

Entanglement resembles Bell states rather than Fock states.

Abstract

In a recent paper (arXiv:1905.07348v1), Dyson scheme to deal with density matrix of non-Hermitian Hamiltonians has been used to investigate the entanglement of states of a PT-symmetric bosonic system. They found that von Neumann entropy can show a different behavior in the broken and unbroken regime. We show that their results can be recast in terms of an abstract model of pseudo-Hermitian random matrices. It is found however that, although the formalism is practically the same, the entanglement is not of Fock states but of Bell states.