Super Quantum Discord and Inferior  “Geometric Discord” Based on Weak  Measurement in Noninertial Frames

Maohuai Xiang; Jiliang Jing

doi:10.4236/jqis.2014.41005

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Journal of Quantum Information Science > Vol.4 No.1, March 2014

Super Quantum Discord and Inferior “Geometric Discord” Based on Weak Measurement in Noninertial Frames ()

Department of Physics, and Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha, China.

DOI: 10.4236/jqis.2014.41005 PDF HTML XML 3,701 Downloads 5,272 Views Citations

Abstract

Instead of projective measurement, we use weak measurement to define quantum and geometric discords, and compare them with the normal quantum and geometric discords based on the projective measurement in noninertial frames. We find that using weak measurement to define quantum discord we can capture more quantum correlations compared with the projective measurement, so calling it super quantum discord. However, we note that the geometric discord based on the weak measurements becomes smaller, so we name it inferior “geometric discord”. We also show that, although both the super quantum discord and the inferior “geometric discord” decrease with the increase of observer’s acceleration, the super quantum discord/inferior “geometric discord” increases/decreases as the measurements become weak. These differences reveal that the definitions of the quantum and geometric discords are not too concordant with each other.

Keywords

Weak Measurement; Super Quantum Discord; Inferior; Geometric Discord

Share and Cite:

Xiang, M. and Jing, J. (2014) Super Quantum Discord and Inferior “Geometric Discord” Based on Weak Measurement in Noninertial Frames. Journal of Quantum Information Science, 4, 54-63. doi: 10.4236/jqis.2014.41005.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Peres, A. and Terno, D.R. (2004) Quantum Information and Relativity Theory. Reviews of Modern Physics, 76, 93-123. http://dx.doi.org/10.1103/RevModPhys.76.93
[2]	Bouwmeester, D., Ekert, A. and Zeilinger, A. (2000) The Physics of Quantum Information. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-662-04209-0
[3]	Alsing, P.M. and Milburn, G.J. (2003) Teleportation with a Uniformly Accelerated Partner. Physical Review Letters, 91, Article ID: 180404. http://dx.doi.org/10.1103/PhysRevLett.91.180404
[4]	Fuentes-Schuller, I. and Mann, R.B. (2005) Alice Falls into a Black Hole: Entanglement in Noninertial Frames. Physical Review Letters, 95, Article ID: 120404. http://dx.doi.org/10.1103/PhysRevLett.95.120404
[5]	Pan, Q. and Jing, J. (2008) Degradation of Nonmaximal Entanglement of Scalar and Dirac Fields in Noninertial Frames. Physical Review A, 77, Article ID: 024302.
[6]	Alsing, P.M., Fuentes-Schuller, I., Mann, R.B. and Tessier, T.E. (2006) Entanglement of Dirac Fields in Noninertial Frames. Physical Review A, 74, Article ID: 032326. http://dx.doi.org/10.1103/PhysRevA.74.032326
[7]	Bruschi, D.E., Louko, J., Martn-Martnez, E., Dragan, A. and Fuentes, I. (2010) Unruh Effect in Quantum Information beyond the Single-Mode Approximation. Physical Review A, 82, Article ID: 042332. http://dx.doi.org/10.1103/PhysRevA.82.042332
[8]	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
[9]	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
[10]	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
[11]	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
[12]	Henderson, L. and Vedral, V. (2001) Classical, Quantum and Total Correlations. Journal of Physics A: Mathematical and General, 34, 6899. http://dx.doi.org/10.1088/0305-4470/34/35/315
[13]	Zurek, W.H. (2003) Quantum Discord and Maxwell’s Demons. Physical Review A, 67, Article ID: 012320. http://dx.doi.org/10.1103/PhysRevA.67.012320
[14]	Datta, A. (2009) Quantum Discord between Relatively Accelerated Observers. Physical Review A, 80, Article ID: 052304. http://dx.doi.org/10.1103/PhysRevA.80.052304
[15]	Wang, J., Deng, J. and Jing, J. (2010) Classical Correlation and Quantum Discord Sharing of Dirac Fields in Noninertial Frames. Physical Review A, 81, Article ID: 052120. http://dx.doi.org/10.1103/PhysRevA.81.052120
[16]	Dakic, B., Vedral, V. andBrukner, C. (2010) Necessary and Sufficient Condition for Nonzero Quantum Discord. Physical Review Letters, 105, Article ID: 190502. http://dx.doi.org/10.1103/PhysRevLett.105.190502
[17]	Luo, S. and Fu, S. (2010) Geometric Measure of Quantum Discord. Physical Review A, 82, Article ID: 034302. http://dx.doi.org/10.1103/PhysRevA.82.034302
[18]	Brown, E.G., Cormier, K., Martin-Martinez, E. and Mann, R.B. (2012) Vanishing Geometric Discord in Noninertial Frames. Physical Review A, 86, Article ID: 032108. http://dx.doi.org/10.1103/PhysRevA.86.032108
[19]	Tian, Z. and Jing, J. (2013) Measurement-Induced-Nonlocality via the Unruh Effect. Annals of Physics, 333, 76. http://dx.doi.org/10.1016/j.aop.2013.02.001
[20]	Okrasa, M. and Walczak, Z. (2012) On Two-Qubit States Ordering with Quantum Discords. EPL (Europhysics Letters), 98, 40003. http://dx.doi.org/10.1209/0295-5075/98/40003
[21]	Piani, M. (2012) Problem with Geometric Discord. Physical Review A, 86, Article ID: 034101. http://dx.doi.org/10.1103/PhysRevA.86.034101
[22]	Aharonov, Y., Albert, D.Z. and Vaidman, L. (1988) How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn out to Be 100. Physical Review Letters, 60, 1351. http://dx.doi.org/10.1103/PhysRevLett.60.1351
[23]	Oreshkov, O. and Brun, T.A. (2005) Weak Measurements Are Universal. Physical Review Letters, 95, Article ID: 110409. http://dx.doi.org/10.1103/PhysRevLett.95.110409
[24]	Hosten, O. and Kwiat, P. (2008) Observation of the Spin Hall Effect of Light via Weak Measurements. Science, 319, 787. http://dx.doi.org/10.1126/science.1152697
[25]	Lundeen, J.S., Sutherland, B., Patel, A., Stewart, C. and Bamber, C. (2011) Direct Measurement of the Quantum Wavefunction. Nature, 474, 188. http://dx.doi.org/10.1038/nature10120
[26]	Sjöqvist, E. (2006) Geometric Phase in Weak Measurements. Physics Letters A, 359, 187-189. http://dx.doi.org/10.1016/j.physleta.2006.06.028
[27]	Singh, U. and Pati, A. (2012) Super Quantum Discord with Weak Measurements. arXiv:1211.0939
[28]	Singh, U. and Pati, A. (2013) Weak Measurement Induced Super Discord Can Resurrect Lost Quantumness. arXiv:1305.4393
[29]	Wang, Y., Ma, T., Fan, H., Fei, S. and Wang, Z. (2014) Super-Quantum Correlation and Geometry for Bell-Diagonal States with Weak Measurements. Quantum Information Process, 13, 283.
[30]	Li, B., Chen, L., Fan, H., Fei, S.M. and Wang, Z.X. (2013) Necessary and Sufficient Condition for Vanishing Super Discord. arXiv:1301.7500
[31]	Huai, L., Li, B., Gu, M., Qu, S. and Fan, H. (2013) Quantum Advantage by Weak Measurements. arXiv:1305.6366
[32]	Hu, M., Fan, H. and Tian, D. (2013) Dual Role of Weak Measurements for Quantum Correlation. arXiv:1304.5074
[33]	Wang, J., Deng, J. and Jing, J. (2010) Classical Correlation and Quantum Discord Sharing of Dirac Fields in Noninertial Frames. Physical Review A, 81, Article ID: 052120. http://dx.doi.org/10.1103/PhysRevA.81.052120
[34]	Martin-Martinez, E., Garay, L.J. and Leon, J. (2010) Unveiling Quantum Entanglement Degradation near a Schwarzschild Black Hole. Physical Review D, 82, Article ID: 064006.
[35]	Wang, J. and Jing, J. (2012) System-Environment Dynamics of X-Type States in Noninertial Frames. Annals of Physics, 327, 283. http://dx.doi.org/10.1016/j.aop.2011.10.002