Entanglement of Grassmannian Coherent States

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.

G. Najarbashi

In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n > 2 degree of nilpotency.Choosing an appropriate weight function, we show that it is possible to construct some wellknown entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor product of GCSs.It is shown that for three level systems, the Grassmann creation and annihilation operators b and b † together with b z form a closed deformed algebra, i.e., SU q (2) with q = e 2πi 3 , which is useful to construct entangled qutrit-states.The same argument holds for three level squeezed states.Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled super coherent states.

S. Sivakumar

Manuel Calixto, Emilio Pérez-Romero

We analyze mathematical and physical properties of a previously introduced (Calixto and Pérez-Romero 2014 J. Phys. A: Math. Theor. 47 023027 ) family of U (4) coherent states (CS). They constitute a matrix version of standard spin U (2) CS when we add an extra (pseudospin) dichotomous degree of freedom: layer, sublattice, two-well, nucleon, etc. Applications to bilayer quantum Hall systems at fractions of filling factor are discussed, where Haldane’s sphere picture is generalized to a Grassmannian picture. We also extend Wehrl’s definition of entropy from Glauber to Grassmannian CS and state a conjecture on the entropy lower bound.

Pablo G. O. Anicich, Horacio Grinberg