Para-Grassmannian Coherent and Squeezed States for Pseudo-Hermitian q-Oscillator and their Entanglement

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 paraGrassmannian 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 pseudoHermitian coherent state introduced, and the method also developed to define pseudoHermitian 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 SUq2(2) and SUq2k(2) and also SUq2k(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.