Entanglement of Pseudo-Hermitian Random States

Arun K. Pati

Cleverson Andrade Goulart, Mauricio Porto Pato

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.

Shengjun Wu

Yusef Maleki

In this paper, q-deformed oscillator for pseudo-Hermitian systems is investigated and pseudo-Hermitian appropriate coherent and squeezed states are studied.Also, some basic properties of these states is surveyed.The over-completeness property of the para-Grassmannian pseudo-Hermitian coherent states (PGPHCSs) examined, and also the stability of coherent and squeezed states discussed.The pseudo-Hermitian supercoherent states as the product of a pseudo-Hermitian bosonic coherent state and a para-Grassmannian pseudo-Hermitian coherent state introduced, and the method also developed to define pseudo-Hermitian supersqueezed states.It is also argued that, for q-oscillator algebra of k + 1 degree of nilpotency based on the changed ladder operators, defined in here, we can obtain deformed SU q 2 (2) and SU q 2k (2) and also SU q 2k (1, 1).Moreover, the entanglement of multilevel para-Grassmannian pseudo-Hermitian coherent state will be considered.This is done by choosing an appropriate weight function, and integrating over tensor product of PGPHCSs.

Sevda Mirzaei, G. Najarbashi, M. A. Fasihi +1 more

We study the entanglement of multiqubit fermionic pseudo-Hermitian coherent states (FPHCSs) described by anticommutative Grassmann numbers. We introduce pseudo-Hermitian versions of well-known maximally entangled pure states, such as Bell, GHZ, Werner, and biseparable states, by integrating over the tensor products of FPHCSs with a suitable choice of Grassmannian weight functions. As an illustration, we apply the proposed method to the tensor product of two- and three-qubit pseudo-Hermitian systems. For a quantitative characteristic of entanglement of such states, we use a measure of entanglement determined by the corresponding concurrence function and average entropy.

Aditi Sen