Entanglement and Quantum Discord of Two Moving Atoms

ABSTRACT

In this paper we discuss two measures for the quantumness of correlations (quantum discord and entanglement) of two isolated moving atoms which are initially in Werner state. We compare and analyze the effect of the atomic motion in quantum discord and entanglement. The results show that the atomic motion related to the field mode structure parameter can make the entanglement and quantum discord evolve periodically. The results also indicate that the entanglement suddenly disappears during the evaluation but quantum discord remains non zero, so quantum discord is considered as indicator of disentanglement.

Cite this paper

Zidan, N. (2014) Entanglement and Quantum Discord of Two Moving Atoms.*Applied Mathematics*, **5**, 2485-2492. doi: 10.4236/am.2014.516240.

Zidan, N. (2014) Entanglement and Quantum Discord of Two Moving Atoms.

References

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http://dx.doi.org/10.1103/PhysRevA.85.052315

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http://dx.doi.org/10.1088/0953-4075/44/1/015503

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http://dx.doi.org/10.1016/j.joems.2012.10.005

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http://dx.doi.org/10.1103/PhysRevA.81.042105

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http://dx.doi.org/10.1103/PhysRevA.82.052320

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[17] Yuan, J.B., Kuang, L.M. and Liao, J.Q. (2010) Amplification of Quantum Discord between Two Uncoupled Qubits in a Common Environment by Phase Decoherence. Journal of Physics B: Atomic, Molecular and Optical Physics, 43, Article ID: 165503.

[18] Hao, X., Ma, C.L. and Sha, J. (2010) Decoherence of Quantum Discord in an Asymmetric-Anisotropy Spin System. Journal of Physics A: Mathematical and Theoretical, 43, Article ID: 425302.

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[20] Mi, Y.J. (2012) Classical Correlation and Quantum Discord in a Two-Qubit System under Dissipation Environments. International Journal of Theoretical Physics, 51, 544-553.

http://dx.doi.org/10.1007/s10773-011-0933-5

[21] Ji, Y.H. and Liu, Y.M. (2013) Investigations into Quantum Correlation of Coupled Qubits in a Squeezed Vacuum Reservoir. Chinese Physics B, 22, Article ID: 020305.

[22] Galve, F., Giorgi, G.L. and Zambrini, R. (2011) Maximally Discordant Mixed States of Two-Qubits. Physical Review A, 83, Article ID: 012102.

http://dx.doi.org/10.1103/PhysRevA.83.012102

[23] Girolami, D. and Adesso, G. (2011) Quantum Discord for General Two-Qubit States: Analytical Progress. Physical Review A, 83, Article ID: 052108.

http://dx.doi.org/10.1103/PhysRevA.83.052108

[24] Schlicher, R.R. (1989) Jaynes-Cummings Model with Atomic Motion. Optics Communications, 70, 97-102.

http://dx.doi.org/10.1016/0030-4018(89)90276-9

[25] Wootters, W.K. (1998) Entanglement of Formation of an Arbi-trary State of Two-Qubits. Physical Review Letters, 80, 2245.

http://dx.doi.org/10.1103/PhysRevLett.80.2245

[26] Henderson, L. and Vedral, V. (2001) Classical, Quantum and Total Correlations. Journal of Physics A: Mathematical and General, 34, 6899.

[27] Sarandy, M.S. (2009) Classical Correlation and Quantum Discord in Critical Systems. Physical Review A, 80, Article ID: 022108.

http://dx.doi.org/10.1103/PhysRevA.80.022108

[1] Bennett, C.H. and Di Vincenzo, D.P. (2000) Quantum Information and Computation. Nature, 404, 247.

http://dx.doi.org/10.1038/35005001

[2] Mayer, D.A. (2000) Sophisticated Quantum Search without Entanglement. Physical Review Letters, 85, 4 p.

[3] Lanyon, B.P., Barbieri, M., Almeida, M.P. and White, A.G. (2008) Experimental Quantum Computing without Entanglement. Physical Review Letters, 101, Article ID: 200501.

http://dx.doi.org/10.1103/PhysRevLett.101.200501

[4] Vedral, V. (2003) Classical Correlations and Entanglement in Quantum Measurements. Physical Review Letters, 90, Article ID: 050401.

http://dx.doi.org/10.1103/PhysRevLett.90.050401

[5] Datta, A., Flammia, S.T. and Caves, C.M. (2005) Entanglement and the Power of One Qubit. Physical Review A, 72, Article ID: 042316.

http://dx.doi.org/10.1103/PhysRevA.72.042316

[6] Ollivier, H. and Zurek, W.H. (2001) Quantum Discord: A Measure of the Quantumness of Correlations. Physical Review Letters, 88, Article ID: 017901.

http://dx.doi.org/10.1103/PhysRevLett.88.017901

[7] Datta, A., Shaji, A. and Caves, C.M. (2008) Quantum Discord and the Power of One Qubit. Physical Review Letters, 100, Article ID: 050502.

http://dx.doi.org/10.1103/PhysRevLett.100.050502

[8] Zidan, N. (2014) Quantum Discord of a Two-Qubit Anisotropy XXZ Heisenberg Chain with Dzyaloshinskii-Moriya Interaction. Journal of Quantum Information Science, 4, 104.

http://dx.doi.org/10.4236/jqis.2014.42011

[9] Berrada, K., Fanchini, F.F. and Abdel-Khalek, S. (2012) Quantum Correlation between Each Qubit in a Two-Atom System and the Environment in Terms of Interatomic Distance. Physical Review A, 85, Article ID: 052315.

http://dx.doi.org/10.1103/PhysRevA.85.052315

[10] Wang, C.-Z., Li, C.-X., Nie, L.-Y. and Li, J.-F. (2011) Classical Correlation and Quantum Discord Mediated by Cavity in Two Coupled Qubit. Journal of Physics B: Atomic, Molecular and Optical Physics, 44, Article ID: 015503.

http://dx.doi.org/10.1088/0953-4075/44/1/015503

[11] Zhang, J.S. and Chen, A.X. (2012) Review of Quantum Discord in Bipartite and Multipartite Systems. Quantum Physics Letters, 1, 69.

[12] Mohamed, A.B. (2013) Pairwise Correlations via Quantum Discord and Its Geometric Measure in a Four-Qubit Spin Chain. Journal of the Egyptian Mathematical Society, 21, 68-74.

http://dx.doi.org/10.1016/j.joems.2012.10.005

[13] Luo, S. (2008) Quantum Discord for Two-Qubit Systems. Physical Review A, 77, Article ID: 042303.

http://dx.doi.org/10.1103/PhysRevA.77.042303

[14] Ali, M., Rau, A.R.P. and Alber, G. (2010) Quantum Discord for Two-Qubit X States. Physical Review A, 81, Article ID: 042105.

http://dx.doi.org/10.1103/PhysRevA.81.042105

[15] Chen, Y.X., Li, S.W. and Yin, Z. (2010) Quantum Correlations in a Clusterlike System. Physical Review A, 82, Article ID: 052320.

http://dx.doi.org/10.1103/PhysRevA.82.052320

[16] Hassan, A., Lari, B. and Joag, P. (2010) Thermal Quantum and Classical Correlations in a Two-Qubit XX Model in a Nonuniform External Magnetic Field. Journal of Physics A: Mathe-matical and Theoretical, 43, Article ID: 485302.

[17] Yuan, J.B., Kuang, L.M. and Liao, J.Q. (2010) Amplification of Quantum Discord between Two Uncoupled Qubits in a Common Environment by Phase Decoherence. Journal of Physics B: Atomic, Molecular and Optical Physics, 43, Article ID: 165503.

[18] Hao, X., Ma, C.L. and Sha, J. (2010) Decoherence of Quantum Discord in an Asymmetric-Anisotropy Spin System. Journal of Physics A: Mathematical and Theoretical, 43, Article ID: 425302.

[19] Sun, Z., Lu, X.M. and Song, L. (2010) Quantum Discord Induced by a Spin Chain with Quantum Phase Transition. Journal of Physics B: Atomic, Molecular and Optical Physics, 43, Article ID: 215504.

[20] Mi, Y.J. (2012) Classical Correlation and Quantum Discord in a Two-Qubit System under Dissipation Environments. International Journal of Theoretical Physics, 51, 544-553.

http://dx.doi.org/10.1007/s10773-011-0933-5

[21] Ji, Y.H. and Liu, Y.M. (2013) Investigations into Quantum Correlation of Coupled Qubits in a Squeezed Vacuum Reservoir. Chinese Physics B, 22, Article ID: 020305.

[22] Galve, F., Giorgi, G.L. and Zambrini, R. (2011) Maximally Discordant Mixed States of Two-Qubits. Physical Review A, 83, Article ID: 012102.

http://dx.doi.org/10.1103/PhysRevA.83.012102

[23] Girolami, D. and Adesso, G. (2011) Quantum Discord for General Two-Qubit States: Analytical Progress. Physical Review A, 83, Article ID: 052108.

http://dx.doi.org/10.1103/PhysRevA.83.052108

[24] Schlicher, R.R. (1989) Jaynes-Cummings Model with Atomic Motion. Optics Communications, 70, 97-102.

http://dx.doi.org/10.1016/0030-4018(89)90276-9

[25] Wootters, W.K. (1998) Entanglement of Formation of an Arbi-trary State of Two-Qubits. Physical Review Letters, 80, 2245.

http://dx.doi.org/10.1103/PhysRevLett.80.2245

[26] Henderson, L. and Vedral, V. (2001) Classical, Quantum and Total Correlations. Journal of Physics A: Mathematical and General, 34, 6899.

[27] Sarandy, M.S. (2009) Classical Correlation and Quantum Discord in Critical Systems. Physical Review A, 80, Article ID: 022108.

http://dx.doi.org/10.1103/PhysRevA.80.022108