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

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

2010-08-28

arxiv.org/abs/1008.4836v2

SIGMA 7:011,2011

Physics

Mathematical Physics

Scientific paper

10.3842/SIGMA.2011.011

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 {\bf GHZ}, {\bf 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 $b^\dag$ together with $b_{z}$ form a closed deformed algebra, i.e., $SU_{q}(2)$ with $q=e^{\frac{2\pi i}{3}}$, 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.

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