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This article is cited in 5 scientific papers (total in 5 papers)
Entanglement of Grassmannian Coherent States for Multi-Partite $n$-Level Systems
Ghader Najarbashi, Yusef Maleki Department of Physics, University of Mohaghegh Ardabili, Ardabil, 179, Iran
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 $b^\dagger$ 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.
Keywords:
entanglement; Grassmannian variables; coherent states.
Received: September 5, 2010; in final form January 19, 2011; Published online January 24, 2011
Citation:
Ghader Najarbashi, Yusef Maleki, “Entanglement of Grassmannian Coherent States for Multi-Partite $n$-Level Systems”, SIGMA, 7 (2011), 011, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma569 https://www.mathnet.ru/eng/sigma/v7/p11
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