Skip to main content
SpringerLink
Log in

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

  • Chapter
  • First Online:
Lectures on General Quantum Correlations and their Applications

Part of the book series: Quantum Science and Technology ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    It is worth to mention here that, if a coherence between Bell states is introduced in the initial two-qubit state, for instance for a state as \(\rho _2=\rho _{AB}^0(0.6,0.8,0.3)\) of Eq. (5), freezing of genuine tripartite correlations occurs for finite time periods, showing a plateau in correspondence of the plateau of zero entanglement [58]. The discussion of this behavior is out of the scopes of this chapter.

References

  1. M.B. Plenio, S. Virmani, Quantum Inf. Comput. 7, 1 (2007)

    MathSciNet  Google Scholar 

  2. G. Benenti, G. Casati, G. Strini, Principles of Quantum Computation and Information (World Scientific, Singapore, 2007)

    Book  MATH  Google Scholar 

  3. R. Alicki, K. Lendi, Quantum Dynamical Semigroups and Applications. Lecture Notes in Physics, vol. 717 (Springer, Berlin, 2007)

    Google Scholar 

  4. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)

    Article  ADS  Google Scholar 

  5. H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, New York, 2002)

    MATH  Google Scholar 

  6. Á. Rivas, S.F. Huelga, M.B. Plenio, Rep. Prog. Phys. 77, 094001 (2014)

    Article  ADS  Google Scholar 

  7. T. Yu, J.H. Eberly, Science 323, 598 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  8. R. Lo Franco, B. Bellomo, S. Maniscalco, G. Compagno, Int. J. Mod. Phys. B 27, 1345053 (2013)

    Article  ADS  Google Scholar 

  9. L. Aolita, F. de Melo, L. Davidovich, Rep. Prog. Phys. 78, 042001 (2015)

    Article  ADS  Google Scholar 

  10. K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)

    Article  ADS  Google Scholar 

  11. G. Adesso, T.R. Bromley, M. Cianciaruso, arXiv:1605.00806 (2016)

  12. R. Lo Franco, G. Compagno, Sci. Rep. 6, 20603 (2016)

    Google Scholar 

  13. R. Lo Franco, G. Compagno, A. Messina, A. Napoli, Open Sys. Inf. Dyn. 13, 463 (2006)

    Article  Google Scholar 

  14. R. Lo Franco, G. Compagno, A. Messina, A. Napoli, Int. J. Quantum Inf. 7, 155 (2009)

    Article  Google Scholar 

  15. R. Lo Franco, G. Compagno, A. Messina, A. Napoli, Phys. Lett. A 374, 2235 (2010)

    Article  ADS  Google Scholar 

  16. L. Amico, R. Fazio, A. Osterloh, V. Vedral, Rev. Mod. Phys. 80, 517576 (2008)

    Article  Google Scholar 

  17. M.C. Tichy, F. Mintert, A. Buchleitner, J. Phys. B At. Mol. Opt. Phys. 44, 192001 (2011)

    Article  ADS  Google Scholar 

  18. T.D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, J.L. O’Brien, Nature 464, 45 (2010)

    Article  ADS  Google Scholar 

  19. N. Gisin, R. Thew, Nat. Photonics 1, 165 (2007)

    Article  ADS  Google Scholar 

  20. V. Vedral, Nat. Phys. 10, 256 (2014)

    Article  Google Scholar 

  21. J.-S. Xu et al., Nat. Commun. 1, 7 (2010a)

    Google Scholar 

  22. T. Werlang, S. Souza, F.F. Fanchini, C.J. Villas, Boas. Phys. Rev. A 80, 024103 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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. B. Bellomo, G. Compagno, A. D’Arrigo, G. Falci, R. Lo, Franco, E. Paladino. Phys. Rev. A 81, 062309 (2010)

    Google Scholar 

  26. J. Laurat, K.S. Choi, H. Deng, C.W. Chou, H.J. Kimble, Phys. Rev. Lett. 99, 180504 (2007)

    Article  ADS  Google Scholar 

  27. M.P. Almeida et al., Science 316, 579 (2007)

    Article  ADS  Google Scholar 

  28. B. Bellomo, R. Lo Franco, G. Compagno. Phys. Rev. Lett. 99, 160502 (2007)

    Google Scholar 

  29. B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 77, 032342 (2008a)

    Google Scholar 

  30. K.M.F. Romero, R. Lo Franco, Phys. Scr. 86, 065004 (2012)

    Google Scholar 

  31. R. Lo Franco, Quantum Inf. Process. 15, 2393 (2016)

    Google Scholar 

  32. Z.-X. Man, Y.-J. Xia, R. Lo Franco, Phys. Rev. A 92, 012315 (2015a)

    Google Scholar 

  33. Z.-X. Man, Y.-J. Xia, R. Lo Franco, Sci. Rep. 5, 13843 (2015b)

    Google Scholar 

  34. B. Bellomo, R. Lo Franco, S. Maniscalco, G. Compagno, Phys. Rev. A 78, 060302(R) (2008b)

    Article  ADS  Google Scholar 

  35. B. Bellomo, R. Lo Franco, G. Compagno, Adv. Sci. Lett. 2, 459 (2009)

    Google Scholar 

  36. P. Haikka, T.H. Johnson, S. Maniscalco, Phys. Rev. A 87, 010103(R) (2013)

    Article  ADS  Google Scholar 

  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. R. Lo Franco, New J. Phys. 17, 081004 (2015)

    Google Scholar 

  39. F. Brito, T. Werlang, New J. Phys. 17, 072001 (2015)

    Article  ADS  Google Scholar 

  40. B. Bylicka, D. Chruściński, S. Maniscalco, Sci. Rep. 4, 5720 (2014)

    Article  Google Scholar 

  41. C. Addis, G. Brebner, P. Haikka, S. Maniscalco, Phys. Rev. A 89, 024101 (2014)

    Article  ADS  Google Scholar 

  42. L. Mazzola, S. Maniscalco, J. Piilo, K.-A. Suominen, B.M. Garraway, Phys. Rev. A 80, 012104 (2009)

    Article  ADS  Google Scholar 

  43. J. Tan, T.H. Kyaw, Y. Yeo, Phys. Rev. A 81, 062119 (2010)

    Article  ADS  Google Scholar 

  44. Z.X. Man, Y.J. Xia, N.B. An, New J. Phys. 12, 033020 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  45. Z.-X. Man, N.B. An, Y.-J. Xia, Phys. Rev. A 90, 062104 (2014)

    Article  ADS  Google Scholar 

  46. Z.-X. Man, N.B. An, Y.-J. Xia, Opt. Express 23, 5763 (2015c)

    Article  ADS  Google Scholar 

  47. C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 93, 042313 (2016)

    Article  ADS  Google Scholar 

  48. B. Bellomo, R. Lo Franco, S. Maniscalco, G. Compagno, Phys. Scr. T140, 014014 (2010)

    Google Scholar 

  49. B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 78, 062309 (2008)

    Google Scholar 

  50. B. Bellomo, G. Compagno, R. Lo Franco, A. Ridolfo, S. Savasta, Phys. Scr. T143, 014004 (2011)

    Google Scholar 

  51. B. Bellomo, G. Compagno, R. Lo Franco, A. Ridolfo, S. Savasta, Int. J. Quantum Inform. 9, 1665 (2011)

    Google Scholar 

  52. J.-S. Xu et al., Phys. Rev. Lett. 104, 100502 (2010b)

    Article  ADS  Google Scholar 

  53. F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda, A.O. Caldeira, Phys. Rev. A 81, 052107 (2010)

    Article  ADS  Google Scholar 

  54. D. Zhou, A. Lang, R. Joynt, Quantum Inf. Process. 9, 727 (2010)

    Article  MathSciNet  Google Scholar 

  55. R. Lo Franco, A. D’Arrigo, G. Falci, G. Compagno, E. Paladino, Phys. Scr. T147, 014019 (2012a)

    Article  ADS  Google Scholar 

  56. P. Bordone, F. Buscemi, C. Benedetti, Fluct. Noise Lett. 11, 1242003 (2012)

    Article  Google Scholar 

  57. R. Lo Franco, B. Bellomo, E. Andersson, G. Compagno, Phys. Rev. A 85, 032318 (2012b)

    Article  ADS  Google Scholar 

  58. B. Leggio, R. Lo Franco, D.O. Soares-Pinto, P. Horodecki, G. Compagno, Phys. Rev. A 92, 032311 (2015)

    Article  ADS  Google Scholar 

  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. M. Mannone, R. Lo Franco, G. Compagno, Phys. Scr. T153, 014047 (2013)

    Google Scholar 

  61. F. Altintas, A. Kurt, R. Eryigit, Phys. Lett. A 377, 53 (2012)

    Article  ADS  Google Scholar 

  62. C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 87, 052328 (2013)

    Google Scholar 

  63. J.H. Wilson, B.M. Fregoso, V.M. Galitski, Phys. Rev. B 85, 174304 (2012)

    Article  ADS  Google Scholar 

  64. B. Bellomo, R. Lo Franco, E. Andersson, J.D. Cresser, G. Compagno, Phys. Scr. T147, 014004 (2012)

    Google Scholar 

  65. J. Trapani, M. Bina, S. Maniscalco, M.G.A. Paris, Phys. Rev. A 91, 022113 (2015)

    Article  ADS  Google Scholar 

  66. A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, Phys. Scr. T153, 014014 (2013)

    Article  ADS  Google Scholar 

  67. A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, Int. J. Quantum Inform. 12, 1461005 (2014)

    Google Scholar 

  68. A. D’Arrigo, R. Lo Franco, G. Benenti, E. Paladino, G. Falci, Ann. Phys. 350, 211 (2014)

    Google Scholar 

  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. J. Trapani, M.G.A. Paris, Phys. Rev. A 93, 042119 (2016)

    Article  ADS  Google Scholar 

  71. C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Int. J. Quantum Inf. 10, 1241005 (2012)

    Article  MathSciNet  Google Scholar 

  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. F. Buscemi, P. Bordone, Phys. Rev. A 87, 042310 (2013)

    Article  ADS  Google Scholar 

  74. M. Rossi, C. Benedetti, M.G.A. Paris, Int. J. Quantum Inf. 12, 1560003 (2014)

    Article  MathSciNet  Google Scholar 

  75. B.-H. Liu et al., Nat. Phys. 7, 931 (2011)

    Article  Google Scholar 

  76. C.E. López, G. Romero, F. Lastra, E. Solano, J.C. Retamal, Phys. Rev. Lett. 101, 080503 (2008)

    Article  Google Scholar 

  77. C.E. López, G. Romero, J.C. Retamal, Phys. Rev. A 81, 062114 (2010)

    Article  ADS  Google Scholar 

  78. A. Chiuri, C. Greganti, L. Mazzola, M. Paternostro, P. Mataloni, Sci. Rep. 2, 968 (2012)

    Article  ADS  Google Scholar 

  79. J.H. Reina, C.E. Susa, F.F. Fanchini, Sci. Rep. 4, 7443 (2014)

    Article  ADS  Google Scholar 

  80. R. Lo Franco, A. D’Arrigo, G. Falci, G. Compagno, E. Paladino, Phys. Rev. B 90, 054304 (2014)

    Article  ADS  Google Scholar 

  81. R.L. Franco, A. D’Arrigo, G. Falci, G. Compagno, E. Paladino, Phys. Scr. T153, 014043 (2013)

    Article  ADS  Google Scholar 

  82. G. Kurizki, P. Bertet, Y. Kubo, K. Mlmer, D. Petrosyan, P. Rabl, J. Schmiedmayer, PNAS 112, 3866 (2015)

    Article  ADS  Google Scholar 

  83. G.J. Milburn, Phil. Trans. R. Soc. A 370, 4469 (2012)

    Article  ADS  Google Scholar 

  84. D. Pavlovic, Proc. Sym. App. Math. 71, 233 (2012)

    Article  Google Scholar 

  85. C. Altafini, F. Ticozzi, I.E.E.E. Trans, Autom. Control 57, 1898 (2012)

    Article  Google Scholar 

  86. A. Beggi, F. Buscemi, P. Bordone, Quantum Inf. Process. 1–33 (2016). doi:10.1007/s11128-016-1334-8

  87. C. Benedetti, F. Buscemi, P. Bordone, M.G.A. Paris, Phys. Rev. A 89, 032114 (2014)

    Article  ADS  Google Scholar 

  88. C. Benedetti, M.G.A. Paris, Phys. Lett. A 378, 2495 (2014a)

    Article  ADS  Google Scholar 

  89. C. Benedetti, M.G.A. Paris, Int. J. Quantum Inf. 12, 1461004 (2014b)

    Article  MathSciNet  Google Scholar 

  90. D. Calvani, A. Cuccoli, N.I. Gidopoulos, P. Verrucchi, PNAS 110, 6748 (2013)

    Article  ADS  Google Scholar 

  91. E. Andersson, J.D. Cresser, M.J. Hall, J. Mod. Opt. 54, 1695 (2007)

    Article  ADS  Google Scholar 

  92. J.D. Cresser, C. Facer, Opt. Commun. 283, 773 (2010)

    Article  ADS  Google Scholar 

  93. F.A. Wudarski, P. Nalezyty, G. Sarbicki, D. Chruscinski, Phys. Rev. A 91, 042105 (2015)

    Article  ADS  Google Scholar 

  94. S. Luo, Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  95. B. Bellomo, R. Lo Franco, G. Compagno, Phys. Rev. A 86, 012312 (2012)

    Google Scholar 

  96. B. Aaronson, R. Lo Franco, G. Adesso. Phys. Rev. A 88, 012120 (2013)

    Google Scholar 

  97. B. Aaronson, R. Lo Franco, G. Compagno, G. Adesso, New J. Phys. 15, 093022 (2013)

    Google Scholar 

  98. M. Cianciaruso, T.R. Bromley, W. Roga, R. Lo Franco, G. Adesso, Sci. Rep. 5, 10177 (2015)

    Google Scholar 

  99. W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)

    Article  ADS  Google Scholar 

  100. G. Falci, A. D’Arrigo, A. Mastellone, E. Paladino, Phys. Rev. Lett. 94, 167002 (2005a)

    Article  ADS  Google Scholar 

  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. J. Bylander et al., Nat. Phys. 7, 565 (2011)

    Article  Google Scholar 

  103. F. Chiarello, E. Paladino, M.G. Castellano, C. Cosmelli, A. D’Arrigo, G. Torrioli, G. Falci, New J. Phys. 14, 023031 (2012)

    Article  ADS  Google Scholar 

  104. L.M.K. Vandersypen, I.L. Chuang, Rev. Mod. Phys. 76, 1037 (2005)

    Article  ADS  Google Scholar 

  105. Á. Rivas, S.F. Huelga, M.B. Plenio, Phys. Rev. Lett. 105, 050403 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  106. J. Sun, Y.-N. Sun, C.-F. Li, G.-C. Guo, K. Luoma, J. Piilo, Sci. Bull. 61, 1031 (2016)

    Article  Google Scholar 

  107. C. Addis, F. Ciccarello, M. Cascio, G.M. Palma, S. Maniscalco, New J. Phys. 17, 123004 (2015)

    Article  ADS  Google Scholar 

  108. G. Falci, A. D’Arrigo, A. Mastellone, E. Paladino, Phys. Rev. Lett. 94, 167002 (2005b)

    Article  ADS  Google Scholar 

  109. L. DiCarlo et al., Nature 460, 240 (2009)

    Article  ADS  Google Scholar 

  110. J.-S. Xu et al., Phys. Rev. Lett. 103, 240502 (2009)

    Article  ADS  Google Scholar 

  111. H.-P. Breuer, E.-M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  112. W.H. Zurek, Rev. Mod. Phys. 75, 715 (2003)

    Article  ADS  Google Scholar 

  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. 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. G.L. Giorgi, B. Bellomo, F. Galve, R. Zambrini, Phys. Rev. Lett. 107, 190501 (2011)

    Article  ADS  Google Scholar 

  116. J. Maziero, F.M. Zimmer, Phys. Rev. A 86, 042121 (2012)

    Article  ADS  Google Scholar 

  117. C.H. Bennett, A. Grudka, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 83, 012312 (2011)

    Article  ADS  Google Scholar 

  118. A.C.S. Costa, R.M. Angelo, M.W. Beims, Phys. Rev. A 90, 012322 (2014)

    Article  ADS  Google Scholar 

  119. C.H. Bennett, D.P. DiVincenzo, J.A. Smolin, W.K. Wootters, Phys. Rev. A 54, 3824 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  120. O. Cohen, Phys. Rev. Lett. 80, 2493 (1998)

    Article  ADS  Google Scholar 

  121. A.R.R. Carvalho, M. Busse, O. Brodier, C. Viviescas, A. Buchleitner, Phys. Rev. Lett. 98, 190501 (2007)

    Article  ADS  Google Scholar 

  122. H.-P. Breuer, E.-M. Laine, J. Piilo, B. Vacchini, Rev. Mod. Phys. 88, 021002 (2016)

    Article  ADS  Google Scholar 

  123. S. Haseli, S. Salimi, A.S. Khorashad, Quant. Inf. Process. 14, 3581 (2015)

    Article  ADS  Google Scholar 

  124. M. Ali, Phys. Lett. A 378, 2048 (2014)

    Article  ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Università di Palermo, Viale delle Scienze, Edificio 9, 90128, Palermo, Italy

    Rosario Lo Franco

  2. Dipartimento di Fisica e Chimica, Università di Palermo, via Archirafi 36, 90123, Palermo, Italy

    Rosario Lo Franco & Giuseppe Compagno

Authors
  1. Rosario Lo Franco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giuseppe Compagno
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rosario Lo Franco .

Editor information

Editors and Affiliations

  1. São Paulo State University, São Paulo, Brazil

    Felipe Fernandes Fanchini

  2. São Carlos Institute of Physics, University of São Paulo, São Paulo, Brazil

    Diogo de Oliveira Soares Pinto

  3. School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom

    Gerardo Adesso

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Lo Franco, R., Compagno, G. (2017). Overview on the Phenomenon of Two-Qubit Entanglement Revivals in Classical Environments. In: Fanchini, F., Soares Pinto, D., Adesso, G. (eds) Lectures on General Quantum Correlations and their Applications. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-53412-1_17

Download citation

Publish with us

Policies and ethics

Search

Navigation