Abstract:
In this work, we study a bipartite system composed by a pair of entangled qudits under dephasing, showing how the dynamics can be decoupled into two main sectors. In one of them, the concurrence of the effective state needed to compute the geometric phase generally decays to zero at asymptotic times. Of course, an evolution restricted to this sector can occur or not, depending on the initial state. Among the possibilities, there is a maximally entangled qutrit state (MES) that undergoes a restricted evolution. In this case, instead of decaying to zero, the concurrence as well as the geometric phase signal a transition to an effective two-qubit MES at asymptotic times. Next, we obtain the analytic solution to the master equation for a general initial two-qutrit state, and identify a whole class of decoherence free states. The associated observables, evolving in the presence of the environment, are robust against decoherence regardless of the coupling constants and operating weights. Among them, we obtained all the MES states which are robust against decoherence. The enhanced stability properties around them provides a strategy to minimize the effects of the environment on fractional topological phases. © 2018 Elsevier Inc.
Registro:
Documento: |
Artículo
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Título: | Two-qudit geometric phase evolution under dephasing |
Autor: | Oxman, L.E.; Khoury, A.Z.; Lombardo, F.C.; Villar, P.I. |
Filiación: | Instituto de Física, Universidade Federal Fluminense, Niterói - RJ, 24210-346, Brazil Departamento de Física Juan José Giambiagi, FCEyN UBA and IFIBA CONICET-UBA, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
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Palabras clave: | Decoherence; Entanglement; Geometric phases; Qudits |
Año: | 2018
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Volumen: | 390
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Página de inicio: | 159
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Página de fin: | 179
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DOI: |
http://dx.doi.org/10.1016/j.aop.2018.01.005 |
Título revista: | Annals of Physics
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Título revista abreviado: | Ann. Phys.
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ISSN: | 00034916
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CODEN: | APNYA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00034916_v390_n_p159_Oxman |
Referencias:
- Pancharatnam, S., (1956) Proc. Indian Acad. Sci. A, 44, p. 247
- Berry, M.V., (1984) Proc. R. Soc. A, 392, p. 45
- Simon, R., Mukunda, N., (1993) Phys. Rev. Lett., 70, p. 880
- Mukunda, N., Simon, R., (1993) Ann. Phys., 228, p. 205
- Jones, J.A., Vedral, V., Ekert, A., Castagnoli, G., (2000) Nature, 403, p. 869
- Faoro, L., Siewert, J., Fazio, R., (2003) Phys. Rev. Lett., 90, p. 028301
- Sonier, J.E., (2001) Science, 292, p. 1695
- Solinas, P., Zanardi, P., Zanghi, N., Rossi, F., (2003) Phys. Rev. B, 67, p. 121307
- Shende, V., Bullock, S.S., Markov, I.L., (2006) IEEE Trans. Comput. AID Des., 26, pp. 1000-1010
- Zhang, J., Vala, J., Sastry, S., Whaley, K.B., (2003) Phys. Rev. Lett., 91, p. 027903
- Jordan, S.P., Wocjan, P., (2009) Phys. Rev. A, 80, p. 062301
- Nielsen, M.A., Dowling, M.R., Gu, M., Doherty, A.C., (2006) Phys. Rev. A, 73, p. 062323
- Dowling, M.R., Nielsen, M.A., (2008) Quantum Inf. Comput., 8, pp. 861-899
- Nielsen, M.A., Dowling, M.R., Gu, M., Doherty, A.C., (2006) Science, 311, p. 1133
- Li, B., Yu, Z.-H., Fei, S.-M., (2013) Sci. Rep., 3, p. 2594
- Zanardi, P., Rasetti, M., (1999) Phys. Lett. A, 264, p. 94
- Xiang-Bin, W., Keiji, M., (2001) Phys. Rev. Lett., 87, p. 097901
- Sjöqvist, E., (2012) New J. Phys., 14, p. 103035
- Tong, D.M., Sjöqvist, E., Kwek, L.C., Oh, C.H., (2004) Phys. Rev. Lett., 93, p. 080405
- Tong, D.M., Sjöqvist, E., Kwek, L.C., Oh, C.H., (2005) Phys. Rev. Lett., 95, p. 249902(E)
- Lombardo, F.C., Villar, P.I., (2006) Phys. Rev. A, 74, p. 042311
- Lombardo, F.C., Villar, P.I., (2008) Int. J. Quantum Inf., 6, p. 707713
- Villar, P.I., (2009) Phys. Lett. A, 373, p. 206
- Lombardo, F.C., Villar, P.I., (2010) Phys. Rev. A, 81, p. 022115
- Villar, P.I., Lombardo, F.C., (2011) Phys. Rev. A, 83, p. 052121
- Milman, P., Mosseri, R., (2003) Phys. Rev. Lett., 90, p. 230403
- Milman, P., (2006) Phys. Rev. A, 73, p. 062118
- Johansson, M., Ericsson, M., Singh, K., Sjöqvist, E., Williamson, M.S., (2012) Phys. Rev. A, 85, p. 032112
- Fujiwara, M., Takeoka, M., Mizuno, J., Sasaki, M., (2003) Phys. Rev. Lett., 90, p. 167906
- Cortese, J., (2004) Phys. Rev. A, 69, p. 022302
- Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S., (2002) Phys. Rev. Lett., 88, p. 040404
- Ralph, T.C., Resch, K., Gilchrist, A., (2007) Phys. Rev. A, 75, p. 022313
- Lanyon, B.P., (2008) Phys. Rev. Lett., 100, p. 060504
- Lanyon, B.P., (2009) Nat. Phys., 5, pp. 134-140
- Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N., (2002) Phys. Rev. Lett., 88, p. 127902
- Song, W., Chen, L., Zhu, S.-L., (2009) Phys. Rev. A, 80, p. 012331
- Vertesi, T., Pironio, S., Brunner, N., (2010) Phys. Rev. Lett., 104, p. 060401
- Ivanov, P.A., Kyoseva, E.S., Vitanov, N.V., (2006) Phys. Rev. A, 74, p. 022323
- O'Sullivan-Hale, M.N., Khan, I.A., Boyd, R.W., Howell, J.C., (2005) Phys. Rev. Lett., 94, p. 220501
- Neves, L., Lima, G., Aguirre Gómez, J.G., Monken, C.H., Saavedra, C., Pádua, S., (2005) Phys. Rev. Lett., 94, p. 100501
- Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., O'Connell, A.D., Sank, D., Martinis, J.M., (2009) Science, 325, pp. 722-725
- Oxman, L.E., Khoury, A.Z., (2011) Phys. Rev. Lett., 106, p. 240503
- Rungta, P., Buzek, V., Caves, C.M., Hillery, M., Milburn, G.J., (2001) Phys. Rev. A, 64, p. 042315
- Khoury, A.Z., Oxman, L.E., (2014) Phys. Rev. A, 89, p. 032106
- Oxman, L.E., Khoury, A.Z., (2014) Ann. Physics, 351, p. 138
- Matoso, A.A., Sánchez-Lozano, X., Pimenta, W.M., Machado, P., Marques, B., Sciarrino, F., Oxman, L.E., Pádua, S., (2016) Phys. Rev. A, 94, p. 052305
- Giorgi, H., (1999) Lie Algebras in Particle Physics, Frontiers in Physics
- Breuer, H.-P., Petruccione, F., (2007) The Theory of Open Quantum Systems, , OUP Oxford
- Wootters, W.K., (1998) Phys. Rev. Lett., 80, p. 2245
- Paz, J.P., Zurek, W.H., (2001) Environment Induced Superselection and the Transition from Quantum to Classical in Coherent Matter Waves, Les Houches Session LXXII, EDP Sciences, pp. 533-614. , Kaiser R. Westbrook C. David F. Springer-Verlag Berlin
- Zurek, W.H., (2003) Rev. Modern Phys., 75, p. 715
- Weiss, U., (1999) Quantum Dissipative Systems, , World Scientific Singapore
- Villar, P.I., Lombardo, F.C., (2015) Phys. Lett. A, 379, p. 246
- Lombardo, F.C., Villar, P.I., (2014) Phys. Rev. A, 89, p. 012110
Citas:
---------- APA ----------
Oxman, L.E., Khoury, A.Z., Lombardo, F.C. & Villar, P.I.
(2018)
. Two-qudit geometric phase evolution under dephasing. Annals of Physics, 390, 159-179.
http://dx.doi.org/10.1016/j.aop.2018.01.005---------- CHICAGO ----------
Oxman, L.E., Khoury, A.Z., Lombardo, F.C., Villar, P.I.
"Two-qudit geometric phase evolution under dephasing"
. Annals of Physics 390
(2018) : 159-179.
http://dx.doi.org/10.1016/j.aop.2018.01.005---------- MLA ----------
Oxman, L.E., Khoury, A.Z., Lombardo, F.C., Villar, P.I.
"Two-qudit geometric phase evolution under dephasing"
. Annals of Physics, vol. 390, 2018, pp. 159-179.
http://dx.doi.org/10.1016/j.aop.2018.01.005---------- VANCOUVER ----------
Oxman, L.E., Khoury, A.Z., Lombardo, F.C., Villar, P.I. Two-qudit geometric phase evolution under dephasing. Ann. Phys. 2018;390:159-179.
http://dx.doi.org/10.1016/j.aop.2018.01.005