Microscopic Reversibility, Nonlinearity, and the Conditional Nature of Single Particle Entanglement

  • Giuseppe Di DomenicoEmail author
Part of the Springer Theses book series (Springer Theses)


In 1935 Erwin Schrödinger [1] motivated by the famous paper [2] from Einstein, Podolsky and Rosen (EPR) comment that “Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all.” and he coined the term “entanglement of our knowledge” to describe the inconsistency between the local realism and a quantum mechanical explanation of realty, what Einstein instead terms “quantum-nonlocality”. In 1964 John Bell [3] quantitatively express this violation of local realism obtaining certain bounds (Bell inequalities) for the correlations of measurements on a two-particle systems, that can be directly measured. During the past few decades, there has been attempt to find circumstances in which a single particle is able to show quantum non-locality.


  1. 1.
    Schrödinger Erwin (1935) The present situation in quantum mechanics. Sci Nat 23(68):807–812zbMATHCrossRefGoogle Scholar
  2. 2.
    Einstein Albert, Podolsky Boris, Rosen Nathan (1935) Can quantum-mechanical description of physical reality be considered complete? Phys Rev 47(10):777ADSzbMATHCrossRefGoogle Scholar
  3. 3.
    John S (1964) Bell. On the Einstein Podolsky Rosen paradoxGoogle Scholar
  4. 4.
    Bennett CH, DiVincenzo DP (2000) Quantum information and computation. Nature, 404(6775):247ADSzbMATHCrossRefGoogle Scholar
  5. 5.
    Brunner Nicolas, Cavalcanti Daniel, Pironio Stefano, Scarani Valerio, Wehner Stephanie (2014) Bell nonlocality. Rev Mod Phys 86(2):419ADSCrossRefGoogle Scholar
  6. 6.
    Eisert J (2006) Entanglement in quantum information theory. PhD thesis, University of PotsdamGoogle Scholar
  7. 7.
    Horodecki Ryszard, Horodecki Paweł, Horodecki Michał, Horodecki Karol (2009) Quantum entanglement. Rev Mod Phys 81(2):865ADSMathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Jammer M (1974) Philosophy of quantum mechanics. The interpretations of quantum mechanics in historical perspective. Wiley-Interscience PublicationsGoogle Scholar
  9. 9.
    Aspect Alain, Grangier Philippe, Roger Gérard (1982) Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: a new violation of bell’s inequalities. Phys Rev Lett 49(2):91ADSCrossRefGoogle Scholar
  10. 10.
    Preskill J (1988) Lecture notes on quantum computation.
  11. 11.
    Reiserer Andreas, Kalb Norbert, Rempe Gerhard, Ritter Stephan (2014) A quantum gate between a flying optical photon and a single trapped atom. Nature 508(7495):237–240ADSCrossRefGoogle Scholar
  12. 12.
    Tiecke TG, Thompson JD, de Leon NP, Liu LR, Vuletić V, Lukin MD (2014) Nanophotonic quantum phase switch with a single atom. Nature 508(7495):241–244ADSCrossRefGoogle Scholar
  13. 13.
    Vaidman Lev (1995) Nonlocality of a single photon revisited again. Phys Rev Lett 75(10):2063ADSCrossRefGoogle Scholar
  14. 14.
    Crater HW, Wong CY, Van Alstine P (2006) Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons. Phys Rev D 74(5):054028Google Scholar
  15. 15.
    Deutsch Martin (1951) Evidence for the formation of positronium in gases. Phys Rev 82(3):455ADSCrossRefGoogle Scholar
  16. 16.
    Deutsch Martin, Dulit Everett (1951) Short range interaction of electrons and fine structure of positronium. Phys Rev 84(3):601ADSCrossRefGoogle Scholar
  17. 17.
    Kwiat PG, Mattle K, Weinfurter H, Zeilinger A, Sergienko AV, Shih Y (1995) New high-intensity source of polarization-entangled photon pairs. Phys Rev Lett 75(24):4337ADSCrossRefGoogle Scholar
  18. 18.
    Shih YH, Sergienko AV, Rubin MH, Kiess TE, Alley CO (1994) Two-photon entanglement in type-ii parametric down-conversion. Phys Rev A 50(1):23ADSCrossRefGoogle Scholar
  19. 19.
    Babichev SA, Appel J, Lvovsky AI (2004) Homodyne tomography characterization and nonlocality of a dual-mode optical qubit. Phys Rev Lett 92(19):193601ADSCrossRefGoogle Scholar
  20. 20.
    Fuwa M, Takeda S, Zwierz M, Wiseman HM, Furusawa A (2015) Experimental proof of nonlocal wavefunction collapse for a single particle using homodyne measurements. Nat Commun 6Google Scholar
  21. 21.
    Hardy Lucien (1994) Nonlocality of a single photon revisited. Phys Rev Lett 73(17):2279ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Hessmo Björn, Usachev Pavel, Heydari Hoshang, Björk Gunnar (2004) Experimental demonstration of single photon nonlocality. Phys Rev Lett 92(18):180401ADSCrossRefGoogle Scholar
  23. 23.
    Steve James Jones and Howard Mark Wiseman (2011) Nonlocality of a single photon: paths to an Einstein-Podolsky-Rosen-Steering experiment. Phys Rev A 84(1):012110ADSCrossRefGoogle Scholar
  24. 24.
    Morin Olivier, Bancal Jean-Daniel, Ho Melvyn, Sekatski Pavel, D’Auria Virginia, Gisin Nicolas, Laurat Julien, Sangouard Nicolas (2013) Witnessing trustworthy single-photon entanglement with local homodyne measurements. Phys Rev Lett 110(13):130401ADSCrossRefGoogle Scholar
  25. 25.
    Tan SM, Walls DF, Collett MJ (1991) Nonlocality of a single photon. Phys Rev Lett 66(3):252ADSCrossRefGoogle Scholar
  26. 26.
    Greenberger DM, Horne MA, Zeilinger A (1995) Nonlocality of a single photon? Phys Rev Lett 75(10):2064ADSCrossRefGoogle Scholar
  27. 27.
    Werner RF (1989) Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys Rev A 40(8):4277ADSzbMATHCrossRefGoogle Scholar
  28. 28.
    Van Enk SJ (2005) Single-particle entanglement. Phys Rev A 72(6):064306Google Scholar
  29. 29.
    Drezet Aurélien (2006) Comment on “single-particle entanglement”. Phys Rev A 74(2):026301ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Pawłowski Marcin, Czachor Marek (2006) Degree of entanglement as a physically ill-posed problem: the case of entanglement with vacuum. Phys Rev A 73(4):042111ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Van Enk SJ (2006) Reply to “comment on ‘single-particle entanglement”’. Phys Rev A 74(2):026302ADSCrossRefGoogle Scholar
  32. 32.
    Beugnon J, Jones MP, Dingjan J, Darquié B, Messin G, Browaeys A, Grangier P (2006) Quantum interference between two single photons emitted by independently trapped atoms. Nature, 440(7085):779–782ADSCrossRefGoogle Scholar
  33. 33.
    Feng Xun-Li, Zhang Zhi-Ming, Li Xiang-Dong, Gong Shang-Qing, Zhi-Zhan Xu (2003) Entangling distant atoms by interference of polarized photons. Phys Rev Lett 90(21):217902ADSCrossRefGoogle Scholar
  34. 34.
    Wootters WK, Zurek WH (1982) A single quantum cannot be cloned. Nature, 299(5886):802–803ADSzbMATHCrossRefGoogle Scholar
  35. 35.
    Boschi Danilo, Branca Salvatore, De Martini Francesco, Hardy Lucien, Popescu Sandu (1998) Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett 80(6):1121ADSMathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Bouwmeester Dik, Pan Jian-Wei, Mattle Klaus, Eibl Manfred, Weinfurter Harald, Zeilinger Anton (1997) Experimental quantum teleportation. Nature 390(6660):575–579Google Scholar
  37. 37.
    Vaidman Lev, Yoran Nadav (1999) Methods for reliable teleportation. Phys Rev A 59(1):116ADSCrossRefGoogle Scholar
  38. 38.
    DelRe E, Crosignani B, Di Porto P (2000) Scheme for total quantum teleportation. Phys Rev Lett 84(13):2989ADSCrossRefGoogle Scholar
  39. 39.
    Scully MO, Englert BG, Bednar CJ (1999) Two-photon scheme for detecting the bell basis using atomic coherence. Phys Rev Lett 83(21):4433ADSCrossRefGoogle Scholar
  40. 40.
    Garziano Luigi, Macrì Vincenzo, Stassi Roberto, Di Stefano Omar, Nori Franco, Savasta Salvatore (2016) One photon can simultaneously excite two or more atoms. Phys Rev Lett 117(4):043601ADSCrossRefGoogle Scholar
  41. 41.
    Asbóth JK, Calsamiglia J, Ritsch H (2005) Computable measure of nonclassicality for light. Phys Rev Lett 94(17):173602Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael

Personalised recommendations