Abstract
The time-dependent Pancharatnam phase and the quantum correlations are studied for the two-qubit system in correlated dephasing environment. We find that in both X-state and Y-state, the rapid changes of the time-dependent Pancharatnam phase are intrinsic in the died and alive phenomena of quantum entanglement described by the concurrence under the exactly same parameters, while the slow changes of the time-dependent Pancharatnam phase correspond to the sudden death of entanglement. The results show that the time-dependent Pancharatnam phase includes the information of quantum correlations.
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Walther, P., et al.: Nature 434, 169 (2005)
Bertoni, A., et al.: Phys. Rev. Lett. 84, 5912 (2000)
Biolatti, E., Iotti, R.C., Zanardi, P., Rossi, F.: Phys. Rev. Lett. 85, 5647 (2000)
Cirac, J.I., Zoller, P. Phys. Rev. Lett 74, 4091 (1995)
Wootters, W.K.: Phys. Rev. Lett. 80, 2245 (1998)
Plenio, M.B., Huelga, S.F., Beige, A., Knight, P.L.: Phys. Rev. A 59, 2468 (1999)
Wang, Z.S., Kwek, L.C., Lai, C.H., Oh, C.H.: Eur. Phys. J. D 33, 285 (2005)
Ollivier, H., Zurek, W.: Phys. Rev. Lett. 88, 017901 (2001)
Henderson, L., Vedral, V.: J. Phys. A 34, 6899 (2001)
Pancharatnam, S.: Proc. Indian Acad. Sci. A 44, 1225 (1956)
Berry, M.V.: Proc. R. Soc. A 392, 45 (1984)
Flindt, C., et al.: Phys. Rev. Lett. 98, 240501 (2007)
Corrielli, G., et al.: Nature 5, 4249 (2014)
Mills, D.L., Cao, J.X., Wu, R.Q.: Phys. Rev. B 75, 205439 (2007)
Qu, D., et al.: Phys. Rev. Lett. 110, 067206 (2013)
Yu, Y.-X., et al.: Phys. C 495, 88 (2013)
Fu, G.L., et al.: Int. J. Theor. Phys. 53, 146 (2014)
Lidar, D.A., Chuang, I.L., Whaley, K.B.: Phys. Rev. Lett. 81, 2594 (1998)
Li, X.-F., Fang, M.F.: Int. J. Theor. Phys. 52, 3635 (2013)
Wang, Z.S., Liu, Q.: Phys. Lett. A 377, 3272 (2013)
Wang, Z.S.: Phys. Rev. A 79, 024304 (2009)
Wang, Z.S., Liu, G.Q., Ji, Y.H.: Phys. Rev. A 79, 054301 (2009)
Xu, H.-L., Ji, Y.H., Wang, Z.S.: Int. J. Theor. Phys. 50, 497 (2011)
Wang, Z.S., et al.: Int. J. Theor. Phys. 51, 2850 (2012)
Li, X.-F., Fang, M.F.: Int. J. Theor. Phys. 53, 2075 (2014)
Wang, Z.S., et al.: Phys. Lett. A 372, 775 (2008)
Liu, Q., et al.: Optik 125, 4814 (2014)
Steffen, M., et al.: Science 313, 1423 (2006)
Nunes, L.H.C.M., Farias, R.L.S., Marino, E.C.: Phys. Lett. A 376, 779 (2012)
Tang, L., Liu, F.: Phys. Lett. A 378, 2074 (2014)
Kiktenko, E.O., Fedorov, A.K., Strakhov, A.A., Man’ko, V.I.: Phys. Lett. A 379, 1409 (2015)
Berkley, A.J., et al.: Science 300, 1548 (2003)
Yang, W.J., et al.: Int. J. Theor. Phys. 50, 260 (2010)
Wang, Z.S., Pan, H.: Quantum Inf. Comput. 15, 951 (2015)
Chen, Z.Q., et al.: Int. J. Theor. Phys. 48, 2904 (2009)
Li, X.-F., et al.: Phys. Rev. A 75, 052312 (2007)
Blais, A., et al.: Phys. Rev. A 69, 062320 (2004)
Blais, A., et al.: Phys. Rev. A 75, 032329 (2007)
Majer, J., et al.: Nature 449, 443 (2007)
Lindblad, G.: Comm. Math. Phys. 48, 119 (1976)
Das, S., Agarwal, G.S.: J. Phys. B 42, 205502 (2009)
Fu, G.L., Liu, X.S., Wang, Z.S.: Int. J. Theor. Phys. 52, 3132 (2013)
Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)
Schrödinger, E.: Proc. Camb. Philos. Soc. 31(555) (1935)
Schrödinger, E.: Proc. Camb. Philos. Soc. 32, 446 (1936)
Bell, J.S.: Phys. (N.Y.) 1, 195 (1964)
Adami, C., Cerf, N.J.: Phys. Rev. A 56, 3470 (1997)
kübler, O., Zeh, H.D.: Ann. Phys. 76, 405 (1973)
Luo, S.L.: Phys. Rev. A 77, 042303 (2008)
Ali, M., Rau, A.R.P., Alber, G.: Phys. Rev. A 81, 042105 (2010)
Acknowledgments
Z. S. Wang thanks the support of the Visiting Scholar Research at University of Macau. This work is supported by the Natural Science Foundation of China under Grant No.11365012 and No. 11565015, the Natural Science Foundation of Jiangxi Province, China under Grant No. 20132BAB202008, the Foundation of Science and Technology of Education Office of Jiangxi Province under No. GJJ13235.
Hui Pan thanks the supports of the Science and Technology Development Fund from Macao SAR (FDCT-068/2014/A2 and FDCT-132/2014/A3), and Multi-Year Research Grants (MYRG2014-00159-FST and MYRG2015-0015-FST) and Start-up Research Grant (SRG- 2013-00033-FST) from Research and Development Office at University of Macau.
Bing Xie thanks the supports of Graduate Student Innovation Foundation of Jiangxi Province under Grant No. YC2014–S150.
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Appendix
Appendix
Under correlated dephasing environment,The analytical solutions of the master (3) are given by
where \(x=-\frac {4({\Gamma }-{\Gamma }_0)}{3}-\frac {2^{1/3}m_1}{3\xi _1}+\frac {\xi _1}{3\times 2^{1/3}}, x_{r}=-\frac {4({\Gamma }-{\Gamma }_0)}{3}+\frac {m_1}{3\times 2^{2/3}\xi _1}-\frac {\xi _1}{6\times 2^{1/3}}, x_{i}=\frac {\sqrt {3}m_1}{3\times 2^{2/3}\xi _1}+\frac {\sqrt {3}\xi _1}{6\times 2^{1/3}}, \xi _1=(16({\Gamma }-{\Gamma }_0)^3-72J^2({\Gamma }-{\Gamma }_0)+576n^2({\Gamma }-{\Gamma }_0)\chi ^2_r +(4(12J^2-4({\Gamma }-{\Gamma }_0)^2+48n^2\chi ^2_r)^3+(16({\Gamma }-{\Gamma }_0)^3-72J^2({\Gamma }-{\Gamma }_0) +576n^2({\Gamma }-{\Gamma }_0)\chi ^2_r)^2)^{1/2})^{1/3},m_1=12J^2-4({\Gamma }-{\Gamma }_0)^2+48n^2\chi ^2_r, \eta =(4J^2+2({\Gamma }-{\Gamma }_0) x+x^2)/(8Jn\chi _r),\eta _r=(4J^2-x_i^2+x_r^2+2x_r({\Gamma }-{\Gamma }_0) )/(8J n\chi _r),\eta _i=(x_i x_r+x_i ({\Gamma }-{\Gamma }_0)/(4J n\chi _r).\) The constants c,c r and c i are determined by the initial conditions (5) for the X-state and (15) for the Y-state. Thus we have c = (−2x i cosχ−4η i J sinχ)/(3(η r −η)x i +3η i (x i −x r )), c r = (−x i cosχ−2η i J sinχ)/(3(η−η r )x i +3η i (x r −x)), c i = ((x−x r ) cosχ−2(η r −η)J sinχ)/(3(η−η r )x i +3η i (x r −x)).
In case of the initial Y-state, the ρ 14(0)=ρ 41(0)=0.
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Xie, B., Zeng, G.R., Pan, H. et al. Pancharatnam Phase and Quantum Correlation for Two-qubit System in Correlated Dephasing Environment. Int J Theor Phys 55, 1474–1491 (2016). https://doi.org/10.1007/s10773-015-2786-9
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DOI: https://doi.org/10.1007/s10773-015-2786-9