Entanglement of Grassmannian Coherent States

In this paper we investigate the entanglement of multi-partite Grassmannian coherent states (GCS) described by Grassmann numbers. Choosing an appropriate weight function, we show that it is possible to construct some entangled pure states, consisting of GHZ, W, Bell, cluster type and biseparable states, by 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 SUq (2) with q = e2 π i / 3 which is useful to construct entangled qutrit-states. The same argument hold for three level squeezed states. Moreover combining the Grassmann and bosonic coherent states we construct maximal entangled supersymmetric coherent states. Finally a comparison with maximal entangled bosonic coherent states is presented and it is shown that in some cases they have fermionic counterpart which are maximal entangled after integration with suitable weight functions.