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Overview on the Phenomenon of Two-Qubit Entanglement Revivals in Classical Environments

  • Rosario Lo FrancoEmail author
  • Giuseppe Compagno
Chapter
Part of the Quantum Science and Technology book series (QST)

Abstract

The occurrence of revivals of quantum entanglement between separated open quantum systems has been shown not only for dissipative non-Markovian quantum environments but also for classical environments in absence of back-action. While the phenomenon is well understood in the first case, the possibility to retrieve entanglement when the composite quantum system is subject to local classical noise has generated a debate regarding its interpretation. This dynamical property of open quantum systems assumes an important role in quantum information theory from both fundamental and practical perspectives. Hybrid quantum-classical systems are in fact promising candidates to investigate the interplay among quantum and classical features and to look for possible control strategies of a quantum system by means of a classical device. Here we present an overview on this topic, reporting the most recent theoretical and experimental results about the revivals of entanglement between two qubits locally interacting with classical environments. We also review and discuss the interpretations provided so far to explain this phenomenon, suggesting that they can be cast under a unified viewpoint.

Notes

Acknowledgements

R.L.F. and G.C. acknowledge Felipe Fanchini, Diogo O. Soares-Pinto and Gerardo Adesso for giving them the possibility to contribute to the present book: Lectures on general quantum correlations and their applications.

References

  1. 1.
    M.B. Plenio, S. Virmani, Quantum Inf. Comput. 7, 1 (2007)MathSciNetGoogle Scholar
  2. 2.
    G. Benenti, G. Casati, G. Strini, Principles of Quantum Computation and Information (World Scientific, Singapore, 2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications. Lecture Notes in Physics, vol. 717 (Springer, Berlin, 2007)Google Scholar
  4. 4.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, New York, 2002)zbMATHGoogle Scholar
  6. 6.
    Á. Rivas, S.F. Huelga, M.B. Plenio, Rep. Prog. Phys. 77, 094001 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    T. Yu, J.H. Eberly, Science 323, 598 (2009)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    R. Lo Franco, B. Bellomo, S. Maniscalco, G. Compagno, Int. J. Mod. Phys. B 27, 1345053 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    L. Aolita, F. de Melo, L. Davidovich, Rep. Prog. Phys. 78, 042001 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    G. Adesso, T.R. Bromley, M. Cianciaruso, arXiv:1605.00806 (2016)
  12. 12.
    R. Lo Franco, G. Compagno, Sci. Rep. 6, 20603 (2016)Google Scholar
  13. 13.
    R. Lo Franco, G. Compagno, A. Messina, A. Napoli, Open Sys. Inf. Dyn. 13, 463 (2006)CrossRefGoogle Scholar
  14. 14.
    R. Lo Franco, G. Compagno, A. Messina, A. Napoli, Int. J. Quantum Inf. 7, 155 (2009)CrossRefGoogle Scholar
  15. 15.
    R. Lo Franco, G. Compagno, A. Messina, A. Napoli, Phys. Lett. A 374, 2235 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517576 (2008)CrossRefGoogle Scholar
  17. 17.
    M.C. Tichy, F. Mintert, A. Buchleitner, J. Phys. B At. Mol. Opt. Phys. 44, 192001 (2011)ADSCrossRefGoogle Scholar
  18. 18.
    T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Nature 464, 45 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    N. Gisin, R. Thew, Nat. Photonics 1, 165 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    V. Vedral, Nat. Phys. 10, 256 (2014)CrossRefGoogle Scholar
  21. 21.
    J.-S. Xu et al., Nat. Commun. 1, 7 (2010a)Google Scholar
  22. 22.
    T. Werlang, S. Souza, F.F. Fanchini, C.J. Villas, Boas. Phys. Rev. A 80, 024103 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    A. Salles, F. de Melo, M.P. Almeida, M. Hor-Meyll, S.P. Walborn, P.H.S. Ribeiro, L. Davidovich, Phys. Rev. A 78, 022322 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    B. Bellomo, G. Compagno, A. D’Arrigo, G. Falci, R. Lo Franco, E. Paladino, Int. J. Quantum Inf. 9, 63 (2011)Google Scholar
  25. 25.
    B. Bellomo, G. Compagno, A. D’Arrigo, G. Falci, R. Lo, Franco, E. Paladino. Phys. Rev. A 81, 062309 (2010)Google Scholar
  26. 26.
    J. Laurat, K.S. Choi, H. Deng, C.W. Chou, H.J. Kimble, Phys. Rev. Lett. 99, 180504 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    M.P. Almeida et al., Science 316, 579 (2007)ADSCrossRefGoogle Scholar
  28. 28.
    B. Bellomo, R. Lo Franco, G. Compagno. Phys. Rev. Lett. 99, 160502 (2007)Google Scholar
  29. 29.
    B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 77, 032342 (2008a)Google Scholar
  30. 30.
    K.M.F. Romero, R. Lo Franco, Phys. Scr. 86, 065004 (2012)Google Scholar
  31. 31.
    R. Lo Franco, Quantum Inf. Process. 15, 2393 (2016)Google Scholar
  32. 32.
    Z.-X. Man, Y.-J. Xia, R. Lo Franco, Phys. Rev. A 92, 012315 (2015a)Google Scholar
  33. 33.
    Z.-X. Man, Y.-J. Xia, R. Lo Franco, Sci. Rep. 5, 13843 (2015b)Google Scholar
  34. 34.
    B. Bellomo, R. Lo Franco, S. Maniscalco, G. Compagno, Phys. Rev. A 78, 060302(R) (2008b)ADSCrossRefGoogle Scholar
  35. 35.
    B. Bellomo, R. Lo Franco, G. Compagno, Adv. Sci. Lett. 2, 459 (2009)Google Scholar
  36. 36.
    P. Haikka, T.H. Johnson, S. Maniscalco, Phys. Rev. A 87, 010103(R) (2013)ADSCrossRefGoogle Scholar
  37. 37.
    C. González-Gutiérrez, R. Román-Ancheyta, D. Espitia, R. Lo Franco, Int. J. Quantum Inform. (in press). Preprint at arXiv:1604.04671 (2016)
  38. 38.
    R. Lo Franco, New J. Phys. 17, 081004 (2015)Google Scholar
  39. 39.
    F. Brito, T. Werlang, New J. Phys. 17, 072001 (2015)ADSCrossRefGoogle Scholar
  40. 40.
    B. Bylicka, D. Chruściński, S. Maniscalco, Sci. Rep. 4, 5720 (2014)CrossRefGoogle Scholar
  41. 41.
    C. Addis, G. Brebner, P. Haikka, S. Maniscalco, Phys. Rev. A 89, 024101 (2014)ADSCrossRefGoogle Scholar
  42. 42.
    L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, B.M. Garraway, Phys. Rev. A 80, 012104 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    J. Tan, T.H. Kyaw, Y. Yeo, Phys. Rev. A 81, 062119 (2010)ADSCrossRefGoogle Scholar
  44. 44.
    Z.X. Man, Y.J. Xia, N.B. An, New J. Phys. 12, 033020 (2010)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Z.-X. Man, N.B. An, Y.-J. Xia, Phys. Rev. A 90, 062104 (2014)ADSCrossRefGoogle Scholar
  46. 46.
    Z.-X. Man, N.B. An, Y.-J. Xia, Opt. Express 23, 5763 (2015c)ADSCrossRefGoogle Scholar
  47. 47.
    C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 93, 042313 (2016)ADSCrossRefGoogle Scholar
  48. 48.
    B. Bellomo, R. Lo Franco, S. Maniscalco, G. Compagno, Phys. Scr. T140, 014014 (2010)Google Scholar
  49. 49.
    B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 78, 062309 (2008)Google Scholar
  50. 50.
    B. Bellomo, G. Compagno, R. Lo Franco, A. Ridolfo, S. Savasta, Phys. Scr. T143, 014004 (2011)Google Scholar
  51. 51.
    B. Bellomo, G. Compagno, R. Lo Franco, A. Ridolfo, S. Savasta, Int. J. Quantum Inform. 9, 1665 (2011)Google Scholar
  52. 52.
    J.-S. Xu et al., Phys. Rev. Lett. 104, 100502 (2010b)ADSCrossRefGoogle Scholar
  53. 53.
    F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda, A.O. Caldeira, Phys. Rev. A 81, 052107 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    D. Zhou, A. Lang, R. Joynt, Quantum Inf. Process. 9, 727 (2010)MathSciNetCrossRefGoogle Scholar
  55. 55.
    R. Lo Franco, A. D’Arrigo, G. Falci, G. Compagno, E. Paladino, Phys. Scr. T147, 014019 (2012a)ADSCrossRefGoogle Scholar
  56. 56.
    P. Bordone, F. Buscemi, C. Benedetti, Fluct. Noise Lett. 11, 1242003 (2012)CrossRefGoogle Scholar
  57. 57.
    R. Lo Franco, B. Bellomo, E. Andersson, G. Compagno, Phys. Rev. A 85, 032318 (2012b)ADSCrossRefGoogle Scholar
  58. 58.
    B. Leggio, R. Lo Franco, D.O. Soares-Pinto, P. Horodecki, G. Compagno, Phys. Rev. A 92, 032311 (2015)ADSCrossRefGoogle Scholar
  59. 59.
    J.-S. Xu, K. Sun, C.-F. Li, X.-Y. Xu, G.-C. Guo, E. Andersson, R. Lo Franco, G. Compagno, Nat. Commun. 4, 2851 (2013)Google Scholar
  60. 60.
    M. Mannone, R. Lo Franco, G. Compagno, Phys. Scr. T153, 014047 (2013)Google Scholar
  61. 61.
    F. Altintas, A. Kurt, R. Eryigit, Phys. Lett. A 377, 53 (2012)ADSCrossRefGoogle Scholar
  62. 62.
    C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 87, 052328 (2013)Google Scholar
  63. 63.
    J.H. Wilson, B.M. Fregoso, V.M. Galitski, Phys. Rev. B 85, 174304 (2012)ADSCrossRefGoogle Scholar
  64. 64.
    B. Bellomo, R. Lo Franco, E. Andersson, J.D. Cresser, G. Compagno, Phys. Scr. T147, 014004 (2012)Google Scholar
  65. 65.
    J. Trapani, M. Bina, S. Maniscalco, M.G.A. Paris, Phys. Rev. A 91, 022113 (2015)ADSCrossRefGoogle Scholar
  66. 66.
    A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, Phys. Scr. T153, 014014 (2013)ADSCrossRefGoogle Scholar
  67. 67.
    A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, Int. J. Quantum Inform. 12, 1461005 (2014)Google Scholar
  68. 68.
    A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, Ann. Phys. 350, 211 (2014)Google Scholar
  69. 69.
    A. Orieux, G. Ferranti, A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, F. Sciarrino, P. Mataloni, Sci. Rep. 5, 8575 (2015)Google Scholar
  70. 70.
    J. Trapani, M.G.A. Paris, Phys. Rev. A 93, 042119 (2016)ADSCrossRefGoogle Scholar
  71. 71.
    C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Int. J. Quantum Inf. 10, 1241005 (2012)MathSciNetCrossRefGoogle Scholar
  72. 72.
    C. Benedetti, M.G.A. Paris, F. Buscemi, P. Bordone, 22nd International Conference on Noise and Fluctuations (ICNF) pp. 1–4 (2013)Google Scholar
  73. 73.
    F. Buscemi, P. Bordone, Phys. Rev. A 87, 042310 (2013)ADSCrossRefGoogle Scholar
  74. 74.
    M. Rossi, C. Benedetti, M.G.A. Paris, Int. J. Quantum Inf. 12, 1560003 (2014)MathSciNetCrossRefGoogle Scholar
  75. 75.
    B.-H. Liu et al., Nat. Phys. 7, 931 (2011)CrossRefGoogle Scholar
  76. 76.
    C.E. López, G. Romero, F. Lastra, E. Solano, J.C. Retamal, Phys. Rev. Lett. 101, 080503 (2008)CrossRefGoogle Scholar
  77. 77.
    C.E. López, G. Romero, J.C. Retamal, Phys. Rev. A 81, 062114 (2010)ADSCrossRefGoogle Scholar
  78. 78.
    A. Chiuri, C. Greganti, L. Mazzola, M. Paternostro, P. Mataloni, Sci. Rep. 2, 968 (2012)ADSCrossRefGoogle Scholar
  79. 79.
    J.H. Reina, C.E. Susa, F.F. Fanchini, Sci. Rep. 4, 7443 (2014)ADSCrossRefGoogle Scholar
  80. 80.
    R. Lo Franco, A. D’Arrigo, G. Falci, G. Compagno, E. Paladino, Phys. Rev. B 90, 054304 (2014)ADSCrossRefGoogle Scholar
  81. 81.
    R.L. Franco, A. D’Arrigo, G. Falci, G. Compagno, E. Paladino, Phys. Scr. T153, 014043 (2013)ADSCrossRefGoogle Scholar
  82. 82.
    G. Kurizki, P. Bertet, Y. Kubo, K. Mlmer, D. Petrosyan, P. Rabl, J. Schmiedmayer, PNAS 112, 3866 (2015)ADSCrossRefGoogle Scholar
  83. 83.
    G.J. Milburn, Phil. Trans. R. Soc. A 370, 4469 (2012)ADSCrossRefGoogle Scholar
  84. 84.
    D. Pavlovic, Proc. Sym. App. Math. 71, 233 (2012)CrossRefGoogle Scholar
  85. 85.
    C. Altafini, F. Ticozzi, I.E.E.E. Trans, Autom. Control 57, 1898 (2012)CrossRefGoogle Scholar
  86. 86.
    A. Beggi, F. Buscemi, P. Bordone, Quantum Inf. Process. 1–33 (2016). doi: 10.1007/s11128-016-1334-8
  87. 87.
    C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 89, 032114 (2014)ADSCrossRefGoogle Scholar
  88. 88.
    C. Benedetti, M.G.A. Paris, Phys. Lett. A 378, 2495 (2014a)ADSCrossRefGoogle Scholar
  89. 89.
    C. Benedetti, M.G.A. Paris, Int. J. Quantum Inf. 12, 1461004 (2014b)MathSciNetCrossRefGoogle Scholar
  90. 90.
    D. Calvani, A. Cuccoli, N.I. Gidopoulos, P. Verrucchi, PNAS 110, 6748 (2013)ADSCrossRefGoogle Scholar
  91. 91.
    E. Andersson, J.D. Cresser, M.J. Hall, J. Mod. Opt. 54, 1695 (2007)ADSCrossRefGoogle Scholar
  92. 92.
    J.D. Cresser, C. Facer, Opt. Commun. 283, 773 (2010)ADSCrossRefGoogle Scholar
  93. 93.
    F.A. Wudarski, P. Nalezyty, G. Sarbicki, D. Chruscinski, Phys. Rev. A 91, 042105 (2015)ADSCrossRefGoogle Scholar
  94. 94.
    S. Luo, Phys. Rev. A 77, 042303 (2008)ADSCrossRefGoogle Scholar
  95. 95.
    B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 86, 012312 (2012)Google Scholar
  96. 96.
    B. Aaronson, R. Lo Franco, G. Adesso. Phys. Rev. A 88, 012120 (2013)Google Scholar
  97. 97.
    B. Aaronson, R. Lo Franco, G. Compagno, G. Adesso, New J. Phys. 15, 093022 (2013)Google Scholar
  98. 98.
    M. Cianciaruso, T.R. Bromley, W. Roga, R. Lo Franco, G. Adesso, Sci. Rep. 5, 10177 (2015)Google Scholar
  99. 99.
    W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  100. 100.
    G. Falci, A. D’Arrigo, A. Mastellone, E. Paladino, Phys. Rev. Lett. 94, 167002 (2005a)ADSCrossRefGoogle Scholar
  101. 101.
    G. Ithier, E. Collin, P. Joyez, P.J. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl et al., Phys. Rev. B 72, 134519 (2005)Google Scholar
  102. 102.
    J. Bylander et al., Nat. Phys. 7, 565 (2011)CrossRefGoogle Scholar
  103. 103.
    F. Chiarello, E. Paladino, M.G. Castellano, C. Cosmelli, A. D’Arrigo, G. Torrioli, G. Falci, New J. Phys. 14, 023031 (2012)ADSCrossRefGoogle Scholar
  104. 104.
    L.M.K. Vandersypen, I.L. Chuang, Rev. Mod. Phys. 76, 1037 (2005)ADSCrossRefGoogle Scholar
  105. 105.
    Á. Rivas, S.F. Huelga, M.B. Plenio, Phys. Rev. Lett. 105, 050403 (2010)ADSMathSciNetCrossRefGoogle Scholar
  106. 106.
    J. Sun, Y.-N. Sun, C.-F. Li, G.-C. Guo, K. Luoma, J. Piilo, Sci. Bull. 61, 1031 (2016)CrossRefGoogle Scholar
  107. 107.
    C. Addis, F. Ciccarello, M. Cascio, G.M. Palma, S. Maniscalco, New J. Phys. 17, 123004 (2015)ADSCrossRefGoogle Scholar
  108. 108.
    G. Falci, A. D’Arrigo, A. Mastellone, E. Paladino, Phys. Rev. Lett. 94, 167002 (2005b)ADSCrossRefGoogle Scholar
  109. 109.
    L. DiCarlo et al., Nature 460, 240 (2009)ADSCrossRefGoogle Scholar
  110. 110.
    J.-S. Xu et al., Phys. Rev. Lett. 103, 240502 (2009)ADSCrossRefGoogle Scholar
  111. 111.
    H.-P. Breuer, E.-M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)ADSMathSciNetCrossRefGoogle Scholar
  112. 112.
    W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003)ADSCrossRefGoogle Scholar
  113. 113.
    F.F. Fanchini, G. Karpat, B. Cakmak, L.K. Castelano, G.H. Aguilar, O.J. Farías, S.P. Walborn, P.H. Souto Ribeiro, M.C. de Oliveira, Phys. Rev. Lett. 112, 210402 (2014)Google Scholar
  114. 114.
    S. Haseli, G. Karpat, S. Salimi, A.S. Khorashad, F.F. Fanchini, B. Cakmak, G.H. Aguilar, S.P. Walborn, P.H. Souto Ribeiro. Phys. Rev. A 90, 052118 (2014)Google Scholar
  115. 115.
    G.L. Giorgi, B. Bellomo, F. Galve, R. Zambrini, Phys. Rev. Lett. 107, 190501 (2011)ADSCrossRefGoogle Scholar
  116. 116.
    J. Maziero, F.M. Zimmer, Phys. Rev. A 86, 042121 (2012)ADSCrossRefGoogle Scholar
  117. 117.
    C.H. Bennett, A. Grudka, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 83, 012312 (2011)ADSCrossRefGoogle Scholar
  118. 118.
    A.C.S. Costa, R.M. Angelo, M.W. Beims, Phys. Rev. A 90, 012322 (2014)ADSCrossRefGoogle Scholar
  119. 119.
    C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)ADSMathSciNetCrossRefGoogle Scholar
  120. 120.
    O. Cohen, Phys. Rev. Lett. 80, 2493 (1998)ADSCrossRefGoogle Scholar
  121. 121.
    A.R.R. Carvalho, M. Busse, O. Brodier, C. Viviescas, A. Buchleitner, Phys. Rev. Lett. 98, 190501 (2007)ADSCrossRefGoogle Scholar
  122. 122.
    H.-P. Breuer, E.-M. Laine, J. Piilo, B. Vacchini, Rev. Mod. Phys. 88, 021002 (2016)ADSCrossRefGoogle Scholar
  123. 123.
    S. Haseli, S. Salimi, A.S. Khorashad, Quant. Inf. Process. 14, 3581 (2015)ADSCrossRefGoogle Scholar
  124. 124.
    M. Ali, Phys. Lett. A 378, 2048 (2014)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Dipartimento di Energia, Ingegneria dell’Informazione e Modelli MatematiciUniversità di PalermoPalermoItaly
  2. 2.Dipartimento di Fisica e ChimicaUniversità di PalermoPalermoItaly

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