Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Quantum Interaction

QI 2013: Quantum Interaction pp 84–96Cite as

Entanglement Zoo I: Foundational and Structural Aspects

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8369))

Abstract

We put forward a general classification for a structural description of the entanglement present in compound entities experimentally violating Bell’s inequalities, making use of a new entanglement scheme that we developed in [1]. Our scheme, although different from the traditional one, is completely compatible with standard quantum theory, and enables quantum modeling in complex Hilbert space for different types of situations. Namely, situations where entangled states and product measurements appear (‘customary quantum modeling’), and situations where states and measurements and evolutions between measurements are entangled (‘nonlocal box modeling’, ‘nonlocal non-marginal box modeling’). The role played by Tsirelson’s bound and marginal distribution law is emphasized. Specific quantum models are worked out in detail in complex Hilbert space within this new entanglement scheme.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Aerts, D., Sozzo, S: Quantum Entanglement in Concept Combinations. Int. J. Theor. Phys. ArXiv:1302.3831 [cs.AI] (2013)

    Google Scholar 

  2. Bell, J.S.: On the einstein-podolsky-rosen paradox. Physics 1, 195–200 (1964)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  6. Aerts, D., Aerts, S.: Applications of quantum statistics in psychological studies of decision processes. Found. Sci. 1, 85–97 (1995)

    MathSciNet  Google Scholar 

  7. 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 

  8. 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 

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

    Google Scholar 

  10. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.): QI 2009. LNCS(LNAI), vol. 5494. Springer, Heidelberg (2009)

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Book  MATH  Google Scholar 

  15. Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.): QI 2011. LNCS, vol. 7052. Springer, Heidelberg (2011)

    MATH  Google Scholar 

  16. 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 

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

    Book  Google Scholar 

  18. Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds.): QI 2012. LNCS, vol. 7620. Springer, Heidelberg (2012)

    MATH  Google Scholar 

  19. Aerts, D.: Example of a macroscopical situation that violates bell inequalities. Lett. Nuovo Cim. 34, 107–111 (1982)

    Article  Google Scholar 

  20. Aerts, D.: The physical origin of the EPR Paradox and How to violate bell inequalities by macroscopical systems. In: Lathi, P., Mittelstaedt, P. (eds.) Symposium on the Foundations of Modern Physics: 50 Years of the Einstein-Podolsky-Rosen Gedankenexperiment, pp. 305–320. World Scientific, Singapore (1985)

    Google Scholar 

  21. Aerts, D.: A possible explanation for the probabilities of quantum mechanics and a macroscopical situation that violates bell inequalities. In: Mittelstaedt, P., Stachow, E.W. (eds.) Recent Developments in Quantum Logic, pp. 235–251. Bibliographisches Institut, mannheim (1985)

    Google Scholar 

  22. 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. Helv. Phys. Acta 64, 1–23 (1991)

    MathSciNet  Google Scholar 

  23. 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 

  24. 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)

    Google Scholar 

  25. Aerts, D., Gabora, L., S. Sozzo, S.: concepts and their dynamics: a quantum-theoretic modeling of human thought. Top. Cogn. Sci. (in print). ArXiv: 1206.1069 [cs.AI]

    Google Scholar 

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

    Article  Google Scholar 

  27. Aerts, D., Sozzo, S.: Entanglement Zoo II. Applications in Physics and Cognition, accepted in LNCS (2013)

    Google Scholar 

  28. Tsirelson, B.S.: Quantum generalizations of bell’s inequality. Lett. Math. Phys. 4, 93–100 (1980)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  30. 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 

  31. Popescu, S., Rohrlich, D.: Nonlocality as an axiom. Found. Phys. 24, 379–385 (1994)

    Article  MathSciNet  Google Scholar 

  32. 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  Google Scholar 

  33. Aerts, S.: A realistic device that simulates the non-local PR box without communication. http://arxiv.org/abs/quant-ph/0504171 (2005)

Download references

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
    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 .

Editor information

Editors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Harald Atmanspacher

  2. School of Management, University of Leicester, Leicester, United Kingdom

    Emmanuel Haven

  3. Queensland University of Technology, Brisbane, Queensland, Australia

    Kirsty Kitto

  4. Department of Physics and Astronomy Centre for Interdisciplinary Science, University of Leicester, Leicester, United Kingdom

    Derek Raine

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Aerts, D., Sozzo, S. (2014). Entanglement Zoo I: Foundational and Structural Aspects. In: Atmanspacher, H., Haven, E., Kitto, K., Raine, D. (eds) Quantum Interaction. QI 2013. Lecture Notes in Computer Science(), vol 8369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54943-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-54943-4_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-54942-7

  • Online ISBN: 978-3-642-54943-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation