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Published in: Quantum Information Processing 1/2015

01-01-2015

Quantum correlation evolution of GHZ and \(W\) states under noisy channels using ameliorated measurement-induced disturbance

Authors: Pakhshan Espoukeh, Pouria Pedram

Published in: Quantum Information Processing | Issue 1/2015

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Abstract

We study quantum correlation of Greenberger–Horne–Zeilinger (GHZ) and W states under various noisy channels using measurement-induced disturbance approach and its optimized version. Although these inequivalent maximal entangled states represent the same quantum correlation in the absence of noise, it is shown that the W state is more robust than the GHZ state through most noisy channels. Also, using measurement-induced disturbance measure, we obtain the analytical relations for the time evolution of quantum correlations in terms of the noisy parameter \(\kappa \) and remove its overestimating quantum correlations upon implementing the ameliorated measurement-induced disturbance.

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Literature
1.
go back to reference Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
2.
go back to reference Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shore, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)ADSCrossRefMathSciNet Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shore, P.W., Smolin, J.A., Wootters, W.K.: Quantum nonlocality without entanglement. Phys. Rev. A 59, 1070 (1999)ADSCrossRefMathSciNet
3.
go back to reference Braunstein, S.L., Caves, C.M., Jozsa, R., Linden, N., Popescu, S., Schack, R.: Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett. 83, 1054 (1999) Braunstein, S.L., Caves, C.M., Jozsa, R., Linden, N., Popescu, S., Schack, R.: Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett. 83, 1054 (1999)
4.
go back to reference Meyer, D.A.: Sophisticated quantum search without entanglement. Phys. Rev. Lett. 85, 2014 (2000) Meyer, D.A.: Sophisticated quantum search without entanglement. Phys. Rev. Lett. 85, 2014 (2000)
5.
go back to reference Biham, E., Brassard, G., Kenigsberg, D., Mor, T.: Quantum computing without entanglement. Theor. Comput. Sci. 320, 15 (2004) Biham, E., Brassard, G., Kenigsberg, D., Mor, T.: Quantum computing without entanglement. Theor. Comput. Sci. 320, 15 (2004)
6.
go back to reference Datta, A., Flammia, S.T., Caves, C.M.: Entanglement and the power of one qubit. Phys. Rev. A 72, 042316 (2005)ADSCrossRef Datta, A., Flammia, S.T., Caves, C.M.: Entanglement and the power of one qubit. Phys. Rev. A 72, 042316 (2005)ADSCrossRef
7.
go back to reference Datta, A., Vidal, G.: On the role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A 75, 042310 (2007)ADSCrossRefMathSciNet Datta, A., Vidal, G.: On the role of entanglement and correlations in mixed-state quantum computation. Phys. Rev. A 75, 042310 (2007)ADSCrossRefMathSciNet
8.
go back to reference Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001) Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)
9.
go back to reference Rajagopal, A.K., Rendell, R.W.: Separability and correlations in composite states based on entropy methods. Phys. Rev. A 66, 022104 (2002)ADSCrossRefMathSciNet Rajagopal, A.K., Rendell, R.W.: Separability and correlations in composite states based on entropy methods. Phys. Rev. A 66, 022104 (2002)ADSCrossRefMathSciNet
10.
go back to reference Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J.: Sen(De), A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 062307 (2005) Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J.: Sen(De), A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 062307 (2005)
11.
go back to reference Devetak, I.: Distillation of local purity from quantum states. Phys. Rev. A 71, 062303 (2005)ADSCrossRef Devetak, I.: Distillation of local purity from quantum states. Phys. Rev. A 71, 062303 (2005)ADSCrossRef
12.
go back to reference Devi, Usha: A.R., Rajagopal, A.K.: Generalized information theoretic measure to discern the quantumness of correlations. Phys. Rev. Lett. 100, 140502 (2008)ADSCrossRefMathSciNet Devi, Usha: A.R., Rajagopal, A.K.: Generalized information theoretic measure to discern the quantumness of correlations. Phys. Rev. Lett. 100, 140502 (2008)ADSCrossRefMathSciNet
13.
go back to reference Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010) Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)
14.
go back to reference Shabani, A.: Lidar, Daniel A.: Vanishing quantum discord is necessary and sufficient for completely positive maps. Phys. Rev. Lett. 102, 100402 (2009)ADSCrossRef Shabani, A.: Lidar, Daniel A.: Vanishing quantum discord is necessary and sufficient for completely positive maps. Phys. Rev. Lett. 102, 100402 (2009)ADSCrossRef
15.
go back to reference Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)ADSCrossRef Rulli, C.C., Sarandy, M.S.: Global quantum discord in multipartite systems. Phys. Rev. A 84, 042109 (2011)ADSCrossRef
16.
go back to reference Giorda, P., Allegra, M.: Paris, Matteo G.A.: Quantum discord for Gaussian states with non-Gaussian measurements. Phys. Rev. A 86, 052328 (2012)ADSCrossRef Giorda, P., Allegra, M.: Paris, Matteo G.A.: Quantum discord for Gaussian states with non-Gaussian measurements. Phys. Rev. A 86, 052328 (2012)ADSCrossRef
17.
go back to reference Terzis, A.F., Androvitsaneas, P., Paspalakis, E.: Thermal quantum discord and classical correlations in a two-qubit Ising model under a site-dependent magnetic field. Quant. Inf. Proc. 11, 1931 (2012)CrossRefMathSciNet Terzis, A.F., Androvitsaneas, P., Paspalakis, E.: Thermal quantum discord and classical correlations in a two-qubit Ising model under a site-dependent magnetic field. Quant. Inf. Proc. 11, 1931 (2012)CrossRefMathSciNet
18.
go back to reference Pinto, J.P.G., Karpat, G., Fanchini, F.F.: Sudden change of quantum discord for a system of two qubits. Phys. Rev. A 88, 034304 (2013)ADSCrossRef Pinto, J.P.G., Karpat, G., Fanchini, F.F.: Sudden change of quantum discord for a system of two qubits. Phys. Rev. A 88, 034304 (2013)ADSCrossRef
19.
go back to reference Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A 83, 052108 (2011) Girolami, D., Adesso, G.: Quantum discord for general two-qubit states: analytical progress. Phys. Rev. A 83, 052108 (2011)
20.
21.
go back to reference Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)ADSCrossRef Ali, M., Rau, A.R.P., Alber, G.: Quantum discord for two-qubit X states. Phys. Rev. A 81, 042105 (2010)ADSCrossRef
22.
go back to reference Ali, M., Rau, A.R.P., Alber, G.: Erratum: Quantum discord for two-qubit X states [Phys. Rev. A 81, 042105 (2010)] Phys. Rev. A 82, 069902(E) (2010). Ali, M., Rau, A.R.P., Alber, G.: Erratum: Quantum discord for two-qubit X states [Phys. Rev. A 81, 042105 (2010)] Phys. Rev. A 82, 069902(E) (2010).
23.
go back to reference Lu, X.-M., Ma, J., Xi, Z., Wang, X.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A 83, 012327 (2011)ADSCrossRef Lu, X.-M., Ma, J., Xi, Z., Wang, X.: Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A 83, 012327 (2011)ADSCrossRef
24.
go back to reference Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. Rev. A 84, 042313 (2011)ADSCrossRef Chen, Q., Zhang, C., Yu, S., Yi, X.X., Oh, C.H.: Quantum discord of two-qubit X states. Phys. Rev. A 84, 042313 (2011)ADSCrossRef
25.
go back to reference Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)ADSCrossRef Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)ADSCrossRef
26.
go back to reference Girolami, D., Paternostro, M., Adesso, G.: Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states. J. Phys. A 44, 352002 (2011)CrossRef Girolami, D., Paternostro, M., Adesso, G.: Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states. J. Phys. A 44, 352002 (2011)CrossRef
27.
go back to reference Greenberger, D.M., Horne, M.A., Zeilinger, A.. In: Kafatos, M. (ed.) Bells theorem, quantum theory, and conceptions of the universe p. 69. Kluwer, Dordrecht (1989). Greenberger, D.M., Horne, M.A., Zeilinger, A.. In: Kafatos, M. (ed.) Bells theorem, quantum theory, and conceptions of the universe p. 69. Kluwer, Dordrecht (1989).
28.
29.
go back to reference Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006) Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006)
31.
go back to reference Jung, E., Hwang, M.-R., Ju, Y.H., Kim, M.-S., Yoo, S.-K., Kim, H., Park, D., Son, J.-W., Tamaryan, S., Cha, S.-K.: Greenberger-Horne-Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78, 012312 (2008) Jung, E., Hwang, M.-R., Ju, Y.H., Kim, M.-S., Yoo, S.-K., Kim, H., Park, D., Son, J.-W., Tamaryan, S., Cha, S.-K.: Greenberger-Horne-Zeilinger versus W states: quantum teleportation through noisy channels. Phys. Rev. A 78, 012312 (2008)
32.
go back to reference Espoukeh, P., Pedram, P.: Quantum teleportation through noisy channels with multi-qubit GHZ states. Quant. Inf. Proc. 13, 1789 (2014). arxiv:1403.1147 Espoukeh, P., Pedram, P.: Quantum teleportation through noisy channels with multi-qubit GHZ states. Quant. Inf. Proc. 13, 1789 (2014). arxiv:​1403.​1147
33.
go back to reference Mahdian, M., Yousefjani, R., Salimi, S.: Quantum discord evolution of three-qubit states under noisy channels. Eur. Phys. J. D 66, 133 (2012)ADSCrossRef Mahdian, M., Yousefjani, R., Salimi, S.: Quantum discord evolution of three-qubit states under noisy channels. Eur. Phys. J. D 66, 133 (2012)ADSCrossRef
Metadata
Title
Quantum correlation evolution of GHZ and states under noisy channels using ameliorated measurement-induced disturbance
Authors
Pakhshan Espoukeh
Pouria Pedram
Publication date
01-01-2015
Publisher
Springer US
Published in
Quantum Information Processing / Issue 1/2015
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-014-0846-3

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