Entanglement of Fermionic Coherent States for Pseudo Hermitian Hamiltonian

In this paper the entanglement of multi-qubit fermionic pseudo Hermitian coherent states (FPHCS) described by anticommutative Grassmann numbers is studied. The pseudo-Hermitian versions of the well-known maximally entangled pure states such as GHZ, W, Bell and biseparable states are introduced through integrating over tensor product of FPHCSs with suitable choice of Grassmannian weight function. Meanwhile to clarify the issue, as an example, a two level pseudo Hermitian Hamiltonian is introduced and using its bi-orthogonal eigen-vectors we construct all possible pseudo Hermitian versions of Bell, W and GHZ states as a tensor product of them. Then using the concurrence measure for two qubit states, entanglement of these states is calculated as a function of the parameters of the pseudo Hermitian Hamiltonian and it is shown that in some special points, the amount of their entanglement coincide with maximal value. Using average entropy the same results are deduced for pseudo W and GHZ states constructed by bi-orthogonal eigen-vectors of pseudo Hermitian Hamiltonian and it is shown that, as a limit point, the maximal values are achieved for Hermitian one.