International Journal of Theoretical Physics

, Volume 53, Issue 10, pp 3587–3603 | Cite as

Quantum Entanglement in Concept Combinations

  • Diederik Aerts
  • Sandro Sozzo


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.


Entanglement Bell inequalities Quantum cognition EPR-Bell experiments 


  1. 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. 2.
    Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1, 195–200 (1964) Google Scholar
  3. 3.
    Aerts, D.: A possible explanation for the probabilities of quantum mechanics. J. Math. Phys. 27, 202–210 (1986) ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    Aerts, D.: The construction of reality and its influence on the understanding of quantum structures. Int. J. Theor. Phys. 31, 1815–1837 (1992) CrossRefMathSciNetGoogle Scholar
  5. 5.
    Aerts, D.: Quantum structures, separated physical entities and probability. Found. Phys. 24, 1227–1259 (1994) ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    Aerts, D.: The hidden measurement formalism: what can be explained and where paradoxes remain. Int. J. Theor. Phys. 37, 291–304 (1998) CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Aerts, D.: Foundations of quantum physics: a general realistic and operational approach. Int. J. Theor. Phys. 38, 289–358 (1999) CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Found. Sci. 1, 85–97 (1994) MathSciNetGoogle Scholar
  9. 9.
    Aerts, D., Broekaert, J., Smets, S.: A quantum structure description of the liar paradox. Int. J. Theor. Phys. 38, 3231–3239 (1999) CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of Bell inequalities in the macroworld. Found. Phys. 30, 1387–1414 (2000) CrossRefMathSciNetGoogle Scholar
  11. 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) CrossRefzbMATHGoogle Scholar
  12. 12.
    Aerts, D., Gabora, L.: A theory of concepts and their combinations II. A Hilbert space representation. Kybernetes 34, 192–221 (2005) CrossRefzbMATHGoogle Scholar
  13. 13.
    Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981) CrossRefGoogle Scholar
  14. 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) CrossRefGoogle Scholar
  15. 15.
    Hampton, J.A.: Disjunction of natural concepts. Mem. Cogn. 16, 579–591 (1988) CrossRefGoogle Scholar
  16. 16.
    Osherson, D.N., Smith, E.E.: Gradedness and conceptual combination. Cognition 12, 299–318 (1982) CrossRefGoogle Scholar
  17. 17.
    Komatsu, L.K.: Recent views on conceptual structure. Psychol. Bull. 112, 500–526 (1992) CrossRefGoogle Scholar
  18. 18.
    Fodor, J.: Concepts: a potboiler. Cognition 50, 95–113 (1994) CrossRefGoogle Scholar
  19. 19.
    Rips, L.J.: The current status of research on concept combination. Mind Lang. 10, 72–104 (1995) CrossRefGoogle Scholar
  20. 20.
    Aerts, D.: Quantum structure in cognition. J. Math. Psychol. 53, 314–348 (2009) CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Aerts, D., D’Hooghe, B., Haven, E.: Quantum experimental data in psychology and economics. Int. J. Theor. Phys. 49, 2971–2990 (2010) CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Aerts, D., Broekaert, J., Gabora, L., Sozzo, S.: Quantum structure and human thought. Behav. Brain Sci. 36, 274–276 (2013) CrossRefGoogle Scholar
  23. 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. 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. 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. 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. 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) CrossRefGoogle Scholar
  28. 28.
    Khrennikov, A.Y.: Ubiquitous Quantum Structure. Springer, Berlin (2010) CrossRefzbMATHGoogle Scholar
  29. 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) zbMATHGoogle Scholar
  30. 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) CrossRefGoogle Scholar
  31. 31.
    Busemeyer, J.R., Bruza, P.D.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012) CrossRefGoogle Scholar
  32. 32.
    Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.) Quantum Interaction. Lecture Notes in Computer Science, vol. 7620 (2012) CrossRefGoogle Scholar
  33. 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) ADSCrossRefGoogle Scholar
  34. 34.
    Accardi, L., Fedullo, A.: On the statistical meaning of complex numbers in quantum theory. Lett. Nuovo Cimento 34, 161–172 (1982) CrossRefMathSciNetGoogle Scholar
  35. 35.
    Pitowsky, I.: Quantum Probability, Quantum Logic. Lecture Notes in Physics, vol. 321. Springer, Berlin (1989) zbMATHGoogle Scholar
  36. 36.
    Peres, A., Terno, D.R.: Quantum information and relativity theory. Rev. Mod. Phys. 76, 93–123 (2004) ADSCrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Masanes, L., Acin, A., Gisin, N.: General properties of nonsignaling theories. Phys. Rev. A 73, 012112 (2006) ADSCrossRefGoogle Scholar
  38. 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. 39.
    Adenier, G., Khrennikov, A.Y.: Is the fair sampling assumption supported by EPR experiments? J. Phys. A 40, 131–141 (2007) CrossRefMathSciNetGoogle Scholar
  40. 40.
    Tsirelson, B.S.: Quantum generalizations of Bell’s inequality. Lett. Math. Phys. 4, 93 (1980) ADSCrossRefMathSciNetGoogle Scholar
  41. 41.
    Aerts, D., Sozzo, S.: Entanglement Zoo I: Foundational and Structural Aspects. LNCS (2014, in print) Google Scholar
  42. 42.
    Aerts, D., Sozzo, S.: Entanglement Zoo II: Examples in Physics and Cognition. LNCS (2014, in print) Google Scholar
  43. 43.
    Aerts, D.: Quantum and concept combination, entangled measurements and prototype theory. Top. Cogn. Sci. (2014, to appear) Google Scholar
  44. 44.
    Aspect, A.: Bell’s inequality test: more ideal than ever. Nature 398, 189–190 (1982) ADSCrossRefGoogle Scholar
  45. 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) ADSCrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Center Leo Apostel (CLEA)Free University of Brussels (VUB)BrusselsBelgium
  2. 2.School of ManagementUniversity of LeicesterLeicesterUK

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