Entanglement of Pseudo-Hermitian Random States

Entropy (Basel). 2020 Sep 30;22(10):1109. doi: 10.3390/e22101109.

Abstract

In a recent paper (A. Fring and T. Frith, Phys. Rev A 100, 101102 (2019)), a 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.

Keywords: PT-symmetry; pseudo-Hermitian operators; quantum information; random matrix theory; von Neumann entropy.