Skip to main content
SpringerLink
Log in

Quantum Entanglement in Concept Combinations

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental data of situations where classical approaches are problematical. In this paper, we analyze the data we collected in an experiment on a specific conceptual combination, showing that Bell’s inequalities are violated in the experiment. We present a new refined entanglement scheme to model these data within standard quantum theory rules, where ‘entangled measurements and entangled evolutions’ occur, in addition to the expected ‘entangled states’, and present a full quantum representation in complex Hilbert space of the data. This stronger form of entanglement in measurements and evolutions might have relevant applications in the foundations of quantum theory, as well as in the interpretation of nonlocality tests. It could indeed explain some non-negligible ‘anomalies’ identified in EPR-Bell experiments.

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. Aerts, D., Sozzo, S.: Quantum structures in cognition: why and how concepts are entangled. In: Lecture Notes in Computer Science, vol. 7052, pp. 118–129. Springer, Berlin (2011)

    Google Scholar 

  2. Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964)

    Google Scholar 

  3. Aerts, D.: A possible explanation for the probabilities of quantum mechanics. J. Math. Phys. 27, 202–210 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  4. Aerts, D.: The construction of reality and its influence on the understanding of quantum structures. Int. J. Theor. Phys. 31, 1815–1837 (1992)

    Article  MathSciNet  Google Scholar 

  5. Aerts, D.: Quantum structures, separated physical entities and probability. Found. Phys. 24, 1227–1259 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  6. Aerts, D.: The hidden measurement formalism: what can be explained and where paradoxes remain. Int. J. Theor. Phys. 37, 291–304 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  7. Aerts, D.: Foundations of quantum physics: a general realistic and operational approach. Int. J. Theor. Phys. 38, 289–358 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Found. Sci. 1, 85–97 (1994)

    MathSciNet  Google Scholar 

  9. Aerts, D., Broekaert, J., Smets, S.: A quantum structure description of the liar paradox. Int. J. Theor. Phys. 38, 3231–3239 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of Bell inequalities in the macroworld. Found. Phys. 30, 1387–1414 (2000)

    Article  MathSciNet  Google Scholar 

  11. Aerts, D., Gabora, L.: A theory of concepts and their combinations I. The structure of the sets of contexts and properties. Kybernetes 34, 167–191 (2005)

    Article  MATH  Google Scholar 

  12. Aerts, D., Gabora, L.: A theory of concepts and their combinations II. A Hilbert space representation. Kybernetes 34, 192–221 (2005)

    Article  MATH  Google Scholar 

  13. Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981)

    Article  Google Scholar 

  14. Hampton, J.A.: Overextension of conjunctive concepts: evidence for a unitary model for concept typicality and class inclusion. J. Exp. Psychol. Learn. Mem. Cogn. 14, 12–32 (1988)

    Article  Google Scholar 

  15. Hampton, J.A.: Disjunction of natural concepts. Mem. Cogn. 16, 579–591 (1988)

    Article  Google Scholar 

  16. Osherson, D.N., Smith, E.E.: Gradedness and conceptual combination. Cognition 12, 299–318 (1982)

    Article  Google Scholar 

  17. Komatsu, L.K.: Recent views on conceptual structure. Psychol. Bull. 112, 500–526 (1992)

    Article  Google Scholar 

  18. Fodor, J.: Concepts: a potboiler. Cognition 50, 95–113 (1994)

    Article  Google Scholar 

  19. Rips, L.J.: The current status of research on concept combination. Mind Lang. 10, 72–104 (1995)

    Article  Google Scholar 

  20. Aerts, D.: Quantum structure in cognition. J. Math. Psychol. 53, 314–348 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  21. Aerts, D., D’Hooghe, B., Haven, E.: Quantum experimental data in psychology and economics. Int. J. Theor. Phys. 49, 2971–2990 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  22. Aerts, D., Broekaert, J., Gabora, L., Sozzo, S.: Quantum structure and human thought. Behav. Brain Sci. 36, 274–276 (2013)

    Article  Google Scholar 

  23. Aerts, D., Gabora, L., Sozzo, S.: Concepts and their dynamics: a quantum-theoretic modeling of human thought. Top. Cogn. Sci. 5, 737–772 (2013)

    Google Scholar 

  24. Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): In: Proceedings of the AAAI Spring Symposium on Quantum Interaction, March 27–29, Stanford University, Stanford (2007)

    Google Scholar 

  25. Bruza, P.D., Lawless, W., van Rijsbergen, C.J., Sofge, D. (eds.): Quantum Interaction: Proceedings of the Second Quantum Interaction Symposium. College Publications, London (2008)

    Google Scholar 

  26. Bruza, P.D., Sofge, D., Lawless, W., Van Rijsbergen, K., Klusch, M. (eds.): Proceedings of the Third Quantum Interaction Symposium. Lecture Notes in Artificial Intelligence, vol. 5494. Springer, Berlin (2009)

    Google Scholar 

  27. Pothos, E.M., Busemeyer, J.R.: A quantum probability model explanation for violations of ‘rational’ decision theory. Proc. R. Soc. B 276, 2171–2178 (2009)

    Article  Google Scholar 

  28. Khrennikov, A.Y.: Ubiquitous Quantum Structure. Springer, Berlin (2010)

    Book  MATH  Google Scholar 

  29. Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.): Quantum Interaction. Lecture Notes in Computer Science, vol. 7052. Springer, Berlin (2011)

    MATH  Google Scholar 

  30. Busemeyer, J.R., Pothos, E., Franco, R., Trueblood, J.S.: A quantum theoretical explanation for probability judgment ‘errors’. Psychol. Rev. 118, 193–218 (2011)

    Article  Google Scholar 

  31. Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  32. Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.) Quantum Interaction. Lecture Notes in Computer Science, vol. 7620 (2012)

    Chapter  Google Scholar 

  33. Clauser, J.F., Horne, M.A., Shimony, A., Holt, R.A.: Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969)

    Article  ADS  Google Scholar 

  34. Accardi, L., Fedullo, A.: On the statistical meaning of complex numbers in quantum theory. Lett. Nuovo Cimento 34, 161–172 (1982)

    Article  MathSciNet  Google Scholar 

  35. Pitowsky, I.: Quantum Probability, Quantum Logic. Lecture Notes in Physics, vol. 321. Springer, Berlin (1989)

    MATH  Google Scholar 

  36. Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76, 93–123 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  37. Masanes, L., Acin, A., Gisin, N.: General properties of nonsignaling theories. Phys. Rev. A 73, 012112 (2006)

    Article  ADS  Google Scholar 

  38. Adenier, G., Khrennikov, A.Y.: Anomalies in EPR-bell experiments. In: Adenier, G., Khrennikov, A.Y., Nieuwenhuizen, T. (eds.) Quantum Theory: Reconsideration of Foundations, vol. 3, pp. 283–293. AIP, New York (2006)

    Google Scholar 

  39. Adenier, G., Khrennikov, A.Y.: Is the fair sampling assumption supported by EPR experiments? J. Phys. A 40, 131–141 (2007)

    Article  MathSciNet  Google Scholar 

  40. Tsirelson, B.S.: Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  41. Aerts, D., Sozzo, S.: Entanglement Zoo I: Foundational and Structural Aspects. LNCS (2014, in print)

  42. Aerts, D., Sozzo, S.: Entanglement Zoo II: Examples in Physics and Cognition. LNCS (2014, in print)

  43. Aerts, D.: Quantum and concept combination, entangled measurements and prototype theory. Top. Cogn. Sci. (2014, to appear)

  44. Aspect, A.: Bell’s inequality test: more ideal than ever. Nature 398, 189–190 (1982)

    Article  ADS  Google Scholar 

  45. Weihs, G., Jennewein, T., Simon, C., Weinfurter, H., Zeilinger, A.: Violation of Bell’s inequality under strict Einstein locality conditions. Phys. Rev. Lett. 81(23), 5039 (1998)

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center Leo Apostel (CLEA), Free University of Brussels (VUB), Krijgskundestraat 33, 1160, Brussels, Belgium

    Diederik Aerts & Sandro Sozzo

  2. School of Management, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Sandro Sozzo

Authors
  1. Diederik Aerts
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sandro Sozzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sandro Sozzo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aerts, D., Sozzo, S. Quantum Entanglement in Concept Combinations. Int J Theor Phys 53, 3587–3603 (2014). https://doi.org/10.1007/s10773-013-1946-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-013-1946-z

Keywords

Search

Navigation