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Entanglement of Conceptual Entities in Quantum Model Theory (QMod)

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Book cover Quantum Interaction (QI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7620))

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Abstract

We have recently elaborated Quantum Model Theory (QMod) to model situations where the quantum effects of contextuality, interference, superposition, entanglement and emergence, appear independently of the microscopic nature of the entities giving rise to these situations. We have shown that QMod models without introducing linearity for the set of the states. In this paper we prove that QMod, although not using linearity for the state space, provides a method of identification for entangled states and an intuitive explanation for their occurrence. We illustrate this method for entanglement identification with concrete examples.

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References

  1. Aerts, D., Sozzo, S.: Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A. (eds.) QI 2012. LNCS, vol. 7620, pp. 126–137. Springer, Heidelberg (2012)

    Google Scholar 

  2. Aerts, D.: Quantum Structure in Cognition. J. Math. Psych. 53, 314–348 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aerts, D.: Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory. Found. Sci. 14, 361–411 (2010)

    Article  MathSciNet  Google Scholar 

  4. Aerts, D.: Interpreting Quantum Particles as Conceptual Entities. Int. J. Theor. Phys. 49, 2950–2970 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Aerts, D.: A Potentiality and Conceptuality Interpretation of Quantum Physics. Philosophica 83, 15–52 (2010)

    Google Scholar 

  6. Aerts, D.: Being and Change: Foundations of a Realistic Operational Formalism. In: Aerts, D., Czachor, M., Durt, T. (eds.) Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics, pp. 71–110. World Scientific, Singapore (2002)

    Chapter  Google Scholar 

  7. Gabora, L., Aerts, D.: Contextualizing Concepts Using a Mathematical Generalization of the Quantum Formalism. J. Exp. Theor. Art. Int. 14, 327–358 (2002)

    Article  MATH  Google Scholar 

  8. 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 

  9. 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 

  10. Gabora, L.: Cultural Evolution Entails (Creativity Entails (Concept Combination Entails Quantum Structure)). In: Bruza, P., Lawless, W., van Rijsbergen, K., Sofge, D. (eds.) Proceedings of the Association for the Advancement of Artificial Intelligence (AAAI) Spring Symposium 8: Quantum Interaction, March 26-28, pp. 106–113. Stanford University, Stanford (2007)

    Google Scholar 

  11. Nelson, D.L.: Entangled Associative Structures and Context. In: Bruza, P., Lawless, W., van Rijsbergen, K., Sofge, D. (eds.) Proceedings of the Association for the Advancement of Artificial Intelligence (AAAI) Spring Symposium 8: Quantum Interaction, March 26-28. Stanford University, Stanford (2007)

    Google Scholar 

  12. Gabora, L., Rosch, E., Aerts, D.: Toward an Ecological Theory of Concepts. Ecol. Psych. 20, 84–116 (2008)

    Article  Google Scholar 

  13. Flender, C., Kitto, K., Bruza, P.: Beyond Ontology in Information Systems. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 276–288. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  14. Gabora, L., Aerts, D.: A Model of the Emergence and Evolution of Integrated Worldviews. J. Math. Psych. 53, 434–451 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. D’Hooghe, B.: The SCOP-formalism: An Operational Approach to Quantum Mechanics. In: AIP Conference Proceedings, vol. 1232, pp. 33–44 (2010)

    Google Scholar 

  16. Aerts, D., Czachor, M., Sozzo, S.: A Contextual Quantum-based Formalism for Population Dynamics. In: Proceedings of the AAAI Fall Symposium (FS-10-08), Quantum Informatics for Cognitive, Social, and Semantic Processes, pp. 22–25 (2010)

    Google Scholar 

  17. Veloz, T., Gabora, L., Eyjolfson, M., Aerts, D.: Toward a Formal Model of the Shifting Relationship between Concepts and Contexts during Associative Thought. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 25–34. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Aerts, D., Sozzo, S.: Quantum Structure in Cognition: Why and How Concepts Are Entangled. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 116–127. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  19. Aerts, D.: A Possible Explanation for the Probabilities of Quantum Mechanics. J. Math. Phys. 27, 202–210 (1986)

    Article  MathSciNet  Google Scholar 

  20. Aerts, D.: Quantum Structures due to Fluctuations of the Measurement Situations. Int. J. Theor. Phys. 32, 2207–2220 (1993)

    Article  MathSciNet  Google Scholar 

  21. Aerts, D.: Quantum Structures, Separated Physical Entities and Probability. Found. Phys. 24, 1227–1259 (1994)

    Article  MathSciNet  Google Scholar 

  22. Aerts, D.: Quantum Structures: An Attempt to Explain Their Appearance in Nature. Int. J. Theor. Phys. 34, 1165–1186 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  23. Aerts, D., Aerts, S.: The Hidden Measurement Formalism: Quantum Mechanics as a Consequence of Fluctuations on the Measurement. In: Ferrero, M., van der Merwe, A. (eds.) New Developments on Fundamental Problems in Quantum Physics, pp. 1–6. Springer, Dordrecht (1997)

    Chapter  Google Scholar 

  24. Aerts, D., Aerts, S., Coecke, B., D’Hooghe, B., Durt, T., Valckenborgh, F.: A Model with Varying Fluctuations in the Measurement Context. In: Ferrero, M., van der Merwe, A. (eds.) New Developments on Fundamental Problems in Quantum Physics, pp. 7–9. Springer, Dordrecht (1997)

    Chapter  Google Scholar 

  25. Aerts, D., Aerts, S., Durt, T., Lévêque, O.: Classical and Quantum Probability in the ε-model. Int. J. Theor. Phys. 38, 407–429 (1999)

    Article  MATH  Google Scholar 

  26. Aerts, S.: Hidden Measurements from Contextual Axiomatics. In: Aerts, D., Czachor, M., Durt, T. (eds.) Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics, pp. 149–164. World Scientific, Singapore (2002)

    Chapter  Google Scholar 

  27. Aerts, S.: The Born Rule from a Consistency Requirement on Hidden Measurements in Complex Hilbert Space. Int. J. Theor. Phys. 44, 999–1009 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  28. Aerts, S.: Quantum and Classical Probability as Bayes-optimal Observation (2006), http://uk.arxiv.org/abs/quant-ph/0601138

  29. Aerts, D.: Example of a macroscopical situation that violates Bell inequalities. Lettere al Nuovo Cimento 34, 107–111 (1982)

    Article  Google Scholar 

  30. Aerts, D.: A mechanistic classical laboratory situation violating the Bell inequalities with 2\(\sqrt{2}\), exactly ‘in the same way’ as its violations by the EPR experiments. Helvetica Physica Acta 64, 1–23 (1991)

    MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Center Leo Apostel (CLEA), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050, Brussels, Belgium

    Diederik Aerts & Sandro Sozzo

Authors
  1. Diederik Aerts
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  2. Sandro Sozzo
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Editor information

Editors and Affiliations

  1. Indiana University, 47405, Bloomington, IN, USA

    Jerome R. Busemeyer

  2. Conservatoire National des Arts et M’etiers, 75003, Paris, France

    François Dubois

  3. Paris School of Economics, 75014, Paris, France

    Ariane Lambert-Mogiliansky

  4. University of Padua, 35131, Padua, Italy

    Massimo Melucci

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Aerts, D., Sozzo, S. (2012). Entanglement of Conceptual Entities in Quantum Model Theory (QMod). In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds) Quantum Interaction. QI 2012. Lecture Notes in Computer Science, vol 7620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35659-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-35659-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35658-2

  • Online ISBN: 978-3-642-35659-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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