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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Authors: Najarbashi, G., Maleki, Yu.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146777
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems / G. Najarbashi, Yu. Maleki // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 32 назв. — англ.

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.