Skip to main content
SpringerLink
Log in

Partial Measurements and the Realization of Quantum-Mechanical Counterfactuals

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic, Dordrecht (1995)

    MATH  Google Scholar 

  2. Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)

    Article  ADS  MATH  Google Scholar 

  3. Peres, A.: J. Mod. Opt. 47, 139 (2000)

    MathSciNet  ADS  Google Scholar 

  4. Peres, A.: Am. J. Phys. 46, 745 (1978)

    Article  ADS  Google Scholar 

  5. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  6. Davies, E.B.: Quantum Theory of Open Systems. Academic Press, New York (1976)

    MATH  Google Scholar 

  7. Ludwig, G.: Einführung in die Grundlagen der Theoretischen Physik, vol. 3. Vieweg, Braunschweig (1976)

    Google Scholar 

  8. Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam (1982)

    MATH  Google Scholar 

  9. Katz, N., Ansmann, M., Bialczak, R.C., Lucero, E., McDermott, R., Neeley, M., Steffen, M., Weig, E.M., Cleland, A.N., Martinis, J.M., Korotkov, A.N.: Science 312, 1498 (2006)

    Article  ADS  Google Scholar 

  10. Jordan, A.N., Korotkov, A.N.: Contemp. Phys. 51, 125 (2010)

    Article  ADS  Google Scholar 

  11. Paraoanu, G.S.: Phys. Rev. Lett. 97, 180406 (2006)

    Article  ADS  Google Scholar 

  12. Kim, Y.-S., Cho, Y.-W., Ra, Y.-S., Kim, Y.-H.: Opt. Express 17, 11978 (2009)

    Article  ADS  Google Scholar 

  13. Korotkov, A.N., Jordan, A.N.: Phys. Rev. Lett. 97, 166805 (2006)

    Article  ADS  Google Scholar 

  14. Katz, N., Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., Oconnell, A., Wang, H., Cleland, A.N., Martinis, J.M., Korotkov, A.N.: Phys. Rev. Lett. 101, 200401 (2008)

    Article  ADS  Google Scholar 

  15. Paraoanu, G.S.: Phys. Rev. B 72, 134528 (2005)

    Article  ADS  Google Scholar 

  16. Paraoanu, G.S.: J. Low Temp. Phys. 146, 263 (2007)

    Article  ADS  Google Scholar 

  17. Feynman, R.P., Leighton, R.B., Sands, M.: The Feynman Lectures on Physics. Addison Wesley, Reading (1964)

    Google Scholar 

  18. Bell, J.S.: Physics 1, 195 (1964)

    Google Scholar 

  19. Bell, J.S.: Rev. Mod. Phys. 38, 447 (1966)

    Article  ADS  MATH  Google Scholar 

  20. Mermin, M.D.: Rev. Mod. Phys. 65, 803 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  21. Leggett, A.J., Garg, A.: Phys. Rev. Lett. 54, 857 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  22. Ruskov, R., Korotkov, A.N., Mizel, A.: Phys. Rev. Lett. 96, 200404 (2006)

    Article  ADS  Google Scholar 

  23. Jordan, A.N., Korotkov, A.N., Büttiker, M.: Phys. Rev. Lett. 97, 026805 (2006)

    Article  ADS  Google Scholar 

  24. Williams, N.S., Jordan, A.N.: Phys. Rev. Lett. 100, 026804 (2008)

    Article  ADS  Google Scholar 

  25. Goggin, M.E., Almeida, M.P., Barbieri, M., Lanyon, B.P., O’Brien, J.L., White, A.G., Pryde, G.J.: arXiv:0907.1679

  26. Ueda, U., Kitagawa, M.: Phys. Rev. Lett. 68, 3424 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  27. Imamoglu, A.: Phys. Rev. A 47, R4577 (1993)

    Article  ADS  Google Scholar 

  28. Aharonov, Y., Anandan, J., Vaidman, L.: Phys. Rev. A 47, 4616 (1993)

    Article  ADS  Google Scholar 

  29. Alter, O., Yamamoto, Y.: Phys. Rev. Lett. 74, 4106 (1995)

    Article  ADS  Google Scholar 

  30. Aharonov, J., Anandan, J., Vaidman, L.: Found. Phys. 26, 117 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  31. d’Ariano, G.M., Yuen, H.P.: Phys. Rev. Lett. 76, 2832 (1996)

    Article  ADS  Google Scholar 

  32. Uffink, J.: Phys. Rev. A 60, 3474 (1999)

    Article  ADS  Google Scholar 

  33. Scully, M.O., Suhail Zubairy, M.: Quantum Optics. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  34. Kraus, K.: Phys. Rev. D 35, 3070 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  35. Uffink, J.: Int. J. Theor. Phys. 33, 199 (1994)

    Article  MathSciNet  Google Scholar 

  36. Andersson, E., Barnett, S.M., Aspect, A.: Phys. Rev. A 72, 042104 (2005)

    Article  ADS  Google Scholar 

  37. Brougham, T., Andersson, E.: Phys. Rev. A 76, 052313 (2007)

    Article  ADS  Google Scholar 

  38. Brougham, T., Andersson, E., Barnett, S.M.: Phys. Rev. A 80, 042106 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  39. Royer, A.: Phys. Rev. Lett. 73, 913 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Royer, A.: Phys. Rev. Lett. 74, 1040(E) (1995)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Hill, S., Wootters, W.K.: Phys. Rev. Lett. 78, 5022 (1997)

    Article  ADS  Google Scholar 

  43. Plenio, M.B., Huelga, S.F., Beige, A., Knight, P.L.: Phys. Rev. A 59, 2468 (1999)

    Article  ADS  Google Scholar 

  44. Li, J., Chalapat, K., Paraoanu, G.S.: Phys. Rev. B 78, 064503 (2008)

    Article  ADS  Google Scholar 

  45. Li, J., Chalapat, K., Paraoanu, G.S.: J. Phys. Conf. Ser. 150, 022051 (2009)

    Article  ADS  Google Scholar 

  46. Pan, J.-W., Bouwmeester, D., Weinfurter, H., Zeilinger, A.: Phys. Rev. Lett. 80, 3891 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. Kaltenbaek, R., Prevedel, R., Aspelmeyer, M., Zeilinger, A.: Phys. Rev. A 79, 040302 (2009)

    Article  ADS  Google Scholar 

  48. Schmid, C., Kiesel, N., Weber, U.K., Ursin, R., Zeilinger, A., Weinfurter, H.: New J. Phys. 11, 033008 (2009)

    Article  ADS  Google Scholar 

  49. Zukowski, M., Zeilinger, A., Horne, M.A., Ekert, A.K.: Phys. Rev. Lett. 71, 4287 (1993)

    Article  ADS  Google Scholar 

  50. Peres, A.: J. Mod. Opt. 47, 139 (2000)

    MathSciNet  ADS  Google Scholar 

  51. Jennewein, T., Weihs, G., Pan, J.-W., Zeilinger, A.: Phys. Rev. Lett. 88, 017903 (2002)

    Article  ADS  Google Scholar 

  52. Jennevein, T., Brukner, C., Aspelmeyer, M., Zeilinger, A.: Int. J. Quantum Inf. 3, 73 (2005)

    Article  Google Scholar 

  53. Paraoanu, G.S.: Found. Phys. doi:10.1007/s10701-010-9513-4

Download references

Author information

Authors and Affiliations

  1. Low Temperature Laboratory, Aalto University, P.O. Box 15100, 00076, Aalto, Finland

    G. S. Paraoanu

  2. Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria

    G. S. Paraoanu

Authors
  1. G. S. Paraoanu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. S. Paraoanu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Paraoanu, G.S. Partial Measurements and the Realization of Quantum-Mechanical Counterfactuals. Found Phys 41, 1214–1235 (2011). https://doi.org/10.1007/s10701-011-9542-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-011-9542-7

Keywords

Search

Navigation