Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 7 (2011), 011, 11 pages      arXiv:1008.4836      https://doi.org/10.3842/SIGMA.2011.011

Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems

Ghader Najarbashi and Yusef Maleki
Department of Physics, University of Mohaghegh Ardabili, Ardabil, 179, Iran

Received September 05, 2010, in final form January 19, 2011; Published online January 24, 2011

Abstract
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 well-known 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 bz form a closed deformed algebra, i.e., SUq(2) with q=e2πi/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.

Key words: entanglement; Grassmannian variables; coherent states.

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