|
SIGMA 7 (2011), 011, 11 pages arXiv:1008.4836
https://doi.org/10.3842/SIGMA.2011.011
Entanglement of Grassmannian Coherent States for Multi-Partite n-Level Systems
Ghader Najarbashi and Yusef Maleki
Department of Physics, University of Mohaghegh Ardabili, Ardabil, 179, Iran
Received September 05, 2010, in final form January 19, 2011; Published online January 24, 2011
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† 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.
Key words:
entanglement; Grassmannian variables; coherent states.
pdf (354 Kb)
tex (14 Kb)
References
- Nielsen M.A., Chuang I.L.,
Quantum computation and quantum information, Cambridge University Press, Cambridge, 2000.
- Petz D.,
Quantum information theory and quantum statistics, Springer-Verlag, Berlin, 2008.
- van Enk S.J.,
Decoherence of multidimensional entangled coherent states,
Phys. Rev. A 72 (2005), 022308, 6 pages,
quant-ph/0503207.
- van Enk S.J., Hirota O.,
Entangled coherent states: teleportation and decoherence,
Phys. Rev. A 64 (2001), 022313, 6 pages,
quant-ph/0012086.
- Fujii K.,
Introduction to coherent states and quantum information theory,
quant-ph/0112090.
- Najarbashi G., Maleki Y.,
Maximal entanglement of two-qubit states constructed by linearly independent coherent states,
arXiv:1007.1387.
- Fu H., Wang X., Solomon A.I.,
Maximal entanglement of nonorthogonal states: classification,
Phys. Lett. A 291 (2001), 73-76,
quant-ph/0105099.
- Wang X., Sanders B.C.,
Multipartite entangled coherent states,
Phys. Rev. A 65 (2001), 012303, 7 pages,
quant-ph/0104011.
- Wang X.,
Bipartite entangled non-orthogonal states,
J. Phys. A: Math. Gen. 35 (2002), 165-173,
quant-ph/0102011.
- Wang X., Sanders B.C., Pan S.-H.,
Entangled coherent states for systems with SU(2) and SU(1,1) symmetries,
J. Phys. A: Math. Gen. 33 (2000), 7451-7467,
quant-ph/0001073.
- Wang X.,
Quantum teleportation of entangled coherent states,
Phys. Rev. A 64 (2001), 022302, 4 pages,
quant-ph/0102048.
- Majid S., Rodríguez-Plaza M.J.,
Random walk and the heat equation on superspace and anyspace,
J. Math. Phys. 35 (1994), 3753-3760.
- Cabra D.C., Moreno E.F., Tanasa A.,
Para-Grassmann variables and coherent states,
SIGMA 2 (2006), 087, 8 pages,
hep-th/0609217.
- Najarbashi G., Fasihi M.A., Fakhri H.,
Generalized Grassmannian coherent states for pseudo-Hermitian n-level systems,
J. Phys. A: Math. Theor. 43 (2010), 325301, 10 pages,
arXiv:1007.1392.
- Borsten L., Dahanayake D., Duff M.J., Rubens W.,
Superqubits,
Phys. Rev. D 81 (2010), 105023, 16 pages,
arXiv:0908.0706.
- Khanna F.C., Malbouisson J.M.C., Santana A.E., Santos E.S.,
Maximum entanglement in squeezed boson and fermion states,
Phys. Rev. A 76 (2007), 022109, 5 pages,
arXiv:0709.0716.
- Castellani L., Grassi P A., Sommovigo L., Quantum computing with superqubits,
arXiv:1001.3753.
- Najarbashi G., Fasihi M.A., Mirmasoudi F., Mirzaei S.,
Entanglement of fermionic coherent states for pseudo Hermitian Hamiltonian, Poster at International Iran Conference on Quantum Information-2010 (2010, Kish Island, Iran).
- Najarbashi G., Maleki Y.,
Entanglement in multi-qubit pure fermionic coherent states,
arXiv:1004.3703.
- Cahill K.E., Glauber R.J.,
Density operators for fermions,
Phys. Rev. A 59 (1999), 1538-1555,
physics/9808029.
- Kerner R.,
Z3-graded algebras and the cubic root of the supersymmetry translations,
J. Math. Phys. 33 (1992), 403-411.
- Filippov A.T., Isaev A.P., Kurdikov A.B.,
Para-Grassmann differential calculus,
Theoret. and Math. Phys. 94 (1993), 150-165,
hep-th/9210075.
- Isaev A.P.,
Para-Grassmann integral, discrete systems and quantum groups,
Internat. J. Modern Phys. A 12 (1997), 201-206,
q-alg/9609030.
- Cugliandolo L.F., Lozano G.S., Moreno E.F., Schaposnik F.A.,
A note on Gaussian integrals over para-Grassmann variables,
Internat. J. Modern Phys. A 19 (2004), 1705-1714,
hep-th/0209172.
- Ilinski K.N., Kalinin G.V., Stepanenko A.S.,
q-functional Wick's theorems for particles with exotic statistics,
J. Phys. A: Math. Gen. 30 (1997), 5299-5310,
hep-th/9704181.
- Barnum H., Knill E., Ortiz G., Somma R., Viola L.,
A subsystem-independent generalization of entanglement,
Phys. Rev. Lett. 92 (2004), 107902, 4 pages,
quant-ph/0305023.
- Munhoz P.P., Semião F.L., Vidiella-Barranco A.,
Cluster-type entangled coherent states,
Phys. Lett. A 372 (2008), 3580-3585,
arXiv:0705.1549.
- Fujii K.,
A relation between coherent states and generalized Bell states,
quant-ph/0105077.
- Gerry C.C., Peart M.,
Spin squeezing and entanglement via hole-burning in atomic coherent states,
Phys. Lett. A 372 (2008), 6480-6483.
- Sun C., Xue K., Wang G., Wu C.,
A study on the relations between the topological parameter and entanglement,
arXiv:1001.4587.
- Ichikawa T., Sasaki T., Tsutsui I., Yonezawa N.,
Exchange symmetry and multipartite entanglement,
Phys. Rev. A 78 (2008), 052105, 8 pages,
arXiv:0805.3625.
- Mandilara A., Akulin V.M., Smilga A.V., Viola L.,
Quantum entanglement via nilpotent polynomials,
Phys. Rev. A 74 (2006), 022331, 34 pages,
quant-ph/0508234.
|
|