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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 011, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.011
(Mi sigma569)
 

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
Full-text PDF (354 kB) Citations (5)
References:
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
Bibliographic databases:
Document Type: Article
MSC: 81R30; 15A75; 81P40
Language: English
Citation: Ghader Najarbashi, Yusef Maleki, “Entanglement of Grassmannian Coherent States for Multi-Partite $n$-Level Systems”, SIGMA, 7 (2011), 011, 11 pp.
Citation in format AMSBIB
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\by Ghader Najarbashi, Yusef Maleki
\paper Entanglement of Grassmannian Coherent States for Multi-Partite $n$-Level Systems
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  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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