Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

• Authors: Lijun Song , Xiaoguang Wang , Dong Yan , Yongda Li
• Languages of publication: EN

Abstracts

EN

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.

Keywords

EN

entanglement conditions; Heisenberg uncertainty relation; Schrödinger-Robertson indeterminacy relation; four-mode states; partial transposition

Discipline

• 03.67.Mn: Entanglement measures, witnesses, and other characterizations(see also 03.65.Ud Entanglement and quantum nonlocality; 42.50.Dv Quantum state engineering and measurements in quantum optics)
• 03.65.Ud: Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)(for entanglement production and manipulation, see 03.67.Bg; for entanglement measures, witnesses etc., see 03.67.Mn; for entanglement in Bose-Einstein condensates, see 03.75.Gg)
• 42.50.Dv: Quantum state engineering and measurements(see also 03.65.Ud Entanglement and quantum nonlocality, e.g., EPR paradox, Bells inequalities, GHZ states, etc.)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2008
• Volume: 6
• Issue: 2
• Pages: 199-204

Dates

published

1 - 6 - 2008

online

26 - 3 - 2008

Contributors

author

Lijun Song

author

Xiaoguang Wang

• Zhejiang Institute of Modern Physics, Department of Physics, Zhejiang University, HangZhou, 310027, P.R.China

author

Dong Yan

• School of Science, Lanzhou University of Technology, Lanzhou, 730050, P.R.China

author

Yongda Li

• School of Science, Changchun University of Science and Technology, Changchun, 130022, P.R.China

References

• [1] M.M. Wolf, G. Giedke, J.I. Cirac, Phys. Rev. Lett. 96, 080502 (2006) [PubMed]
• [2] R. Simon, Phys. Rev. Lett. 84, 2726 (2000) http://dx.doi.org/10.1103/PhysRevLett.84.2726[Crossref]
• [3] L.M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 84, 2722 (2000) http://dx.doi.org/10.1103/PhysRevLett.84.2722[Crossref]
• [4] S. Mancini, V. Giovannetti, D. Vitali, P. Tombesi, Phys. Rev. Lett. 88, 120401 (2002) [PubMed]
• [5] A. Serafini, Phys. Rev. Lett. 96, 110402 (2006) [PubMed]
• [6] A. Gerardo, I. Fabrizio, J. Phys. A: Math. Theor. 40 7821 (2007) http://dx.doi.org/10.1088/1751-8113/40/28/S01[Crossref]
• [7] M. Horodecki et al., Phys. Lett. A 223, 1 (1996) http://dx.doi.org/10.1016/S0375-9601(96)00706-2[Crossref]
• [8] A. Peres, Phys. Rev. Lett. 77, 1413 (1996) http://dx.doi.org/10.1103/PhysRevLett.77.1413[Crossref]
• [9] B. Terhal, Phys. Lett. A 271, 319 (2000) http://dx.doi.org/10.1016/S0375-9601(00)00401-1[Crossref]
• [10] G. Tóth, O. Gühne, Phys. Rev. Lett. 94, 060501 (2005) [PubMed]
• [11] M. A. Jafarizadeh, M. Rezaee, S.K.A. Seyed Yagoobi, Phys. Rev. A 72, 062106 (2005)
• [12] O. Rudolph, arXiv:quant-ph/0202121
• [13] K. Chen, L.A. Wu, Quantum Inf. Comput. 3, 193 (2003)
• [14] H.F. Hofmann, S. Takeuchi, Phys. Rev. A 68, 032103 (2003)
• [15] O. Gühne, Phys. Rev. Lett. 92, 117903 (2004) [PubMed]
• [16] J.S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964)
• [17] J. Clauser, M. Horne, A. Shimony, R. Holt, Phys. Rev. Lett. 23, 880 (1969) http://dx.doi.org/10.1103/PhysRevLett.23.880[Crossref]
• [18] N.D. Mermin, Phys. Rev. Lett. 65, 1838 (1990) http://dx.doi.org/10.1103/PhysRevLett.65.1838[Crossref]
• [19] M. Ardehali, Phys. Rev. A 46, 5375 (1992) http://dx.doi.org/10.1103/PhysRevA.46.5375[Crossref]
• [20] A.V. Belinskii, D.N. Klyshko, Phys. Usp. 36, 653 (1993) http://dx.doi.org/10.1070/PU1993v036n08ABEH002299[Crossref]
• [21] N. Gisin, H. Bechmann-Pasquinucci, Phys. Lett. A 246, 1 (1998) http://dx.doi.org/10.1016/S0375-9601(98)00516-7[Crossref]
• [22] V. Giovannetti, Phys. Rev. A 67, 022320 (2003)
• [23] M. Hillery, M. S. Zubairy, Phys. Rev. Lett. 96, 050503 (2006) [PubMed]
• [24] H. Nha, J. Kim, Phys. Rev. A. 74, 012317 (2006)
• [25] H. Nha, J. Kim, Phys. Rev. A. 75, 012326 (2007)
• [26] G.S. Agarwal, A. Biswas, New J. Phys. 7, 211 (2005) http://dx.doi.org/10.1088/1367-2630/7/1/211[Crossref]
• [27] E. Shchukin, W. Vogel, Phys. Rev. Lett. 95, 230502 (2005) [PubMed]
• [28] E. Schrödinger (Sitzunsber. Preuss. Akad. Wiss., Berlin, 1930) 296
• [29] H.R. Robertson, Phys. Rev. 46, 794 (1934) http://dx.doi.org/10.1103/PhysRev.46.794[Crossref]
• [30] H. Nha, arXiv:quant-ph/07041939
• [31] S.X. Yu, N.L. Liu, Phys. Rev. Lett. 95, 150504 (2004)
• [32] W. Heisenberg, Z. Phys. 43, 122 (1927)
• [33] Z.G. Li, S.M. Fei et al., Phys. Rev. A 75, 012311 (2007)
• [34] X.G. Wang, Phys. Rev. A 64, 012313 (2001)
• [35] W. Dür, G. Vidal, J.I. Cirac, Phys. Rev. A 62, 062314 (2000)
• [36] L.J. Song, X.G. Wang, D. Yan, Z.S. Pu, arXiv:quant-ph/07052264v2

Identifiers

DOI

10.2478/s11534-008-0058-5