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

[摘要] 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 b z form a closed deformed algebra, i.e., SU q (2) with q = e 2π 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.

[关键词] entanglement;Grassmannian variables;coherent states