Applying POVM to Model Non-orthogonality in Quantum Cognition

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• 关键词：Semantic memory ; Bell ; type experiments ; POVM
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9535
• 期：1
• 页码：284-293
• 全文大小：167 KB
• 参考文献：1.Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of bell inequalities in the macroworld. Found. Phys. 30(9), 1387–1414 (2000)MathSciNet CrossRef
  2.Aerts, D., Sozzo, S.: Quantum entanglement in concept combinations. Int. J. Theor. Phys. 53(10), 3587–3603 (2014)MATH MathSciNet CrossRef
  3.Ballentine, L.: Quantum Mechanics: A Modern Development. World Scientific, Singapore (1998)MATH CrossRef
  4.Bruza, P., Kitto, K., Ramm, B., Sitbon, L.: A probabilistic framework for analyzing the compositionality of conceptual combinations. J. Math. Psychol. 67, 26–38 (2015)MathSciNet CrossRef
  5.Bruza, P., Kitto, K., Nelson, D., McEvoy, C.: Is there something quantum-like about the human mental lexicon? J. Math. Psychol. 53, 362–377 (2009)MATH MathSciNet CrossRef
  6.De Muynck, W.M., Martens, H.: Nonideal quantum measurements, simultaneous measurement of incompatible observables, and the Bell inequalities. In: Proceedings of the 3rd International Symposium Foundations of Quantum Mechanics in the Light of New Technology: Central Research Laboratory, Hitachi Ltd, Kokubunji, Tokyo, Japan, 28–31 August 1989, p. 171 (1990)
  7.Dzhafarov, E.N., Kujala, J.V.: Probabilistic contextuality in EPR/Bohm-type systems with signaling allowed. (2014). http://​arxiv.​org/​abs/​1406.​0243
  8.Dzhafarov, E., Kujala, J.: Selectivity in probabilistic causality: where psychology runs into quantum physics. J. Math. Psychol. 56, 54–63 (2012)MATH MathSciNet CrossRef
  9.Gelfand, I., Neumark, M.: On the imbedding of normed rings into the ring of operators in Hilbert space. Rec. Math. [Mat. Sbornik] N.S. 12(54), 197–217 (1943)MathSciNet
  10.Hirsch, F.: Hidden Nonlocality. Ph.D. thesis, University of Geneva (2013). http://​cms.​unige.​ch/​sciences/​physique/​wp-content/​uploads/​Travail-de-Master.​pdf
  11.Khrennikov, A., Basieva, I.: Quantum model for psychological measurements: from the projection postulate to interference of mental observables represented as positive operator valued measures. NeuroQuantology 12(3), 324–336 (2014). http://​www.​neuroquantology.​com/​index.​php/​journal/​article/​view/​750 MathSciNet CrossRef
  12.Khrennikov, A., Basieva, I., Dzhafarov, E.N., Busemeyer, J.R.: Quantum models for psychological measurements: an unsolved problem. Plos One 9(10), e110909 (2014)CrossRef
  13.Kitto, K., Ramm, B., Sitbon, L., Bruza, P.D.: Quantum theory beyond the physical: information in context. Axiomathes 21(2), 331–345 (2011)CrossRef
  14.Kitto, K.: High end complexity. Int. J. Gen. Syst. 37(6), 689–714 (2008)MATH MathSciNet CrossRef
  15.Maudlin, T.: Quantum Non-locality and Relativity: Metaphysical Intimations of Modern Physics, Aristotelian Society Series, vol. 13. Blackwell publishers limited, Oxford, UK (1994)
  16.de Muynck, W.M.: POVMs: a small but important step beyond standard quantum mechanics (2006). http://​arxiv.​org/​abs/​quant-ph/​0608087
  17.Nelson, D.L., Kitto, K., Galea, D., McEvoy, C.L., Bruza, P.D.: How activation, entanglement, and search in semantic memory contribute to event memory. Mem. Cogn. 41(6), 717–819 (2013)CrossRef
  18.Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
  19.Peres, A.: Quantum Theory: Concepts and Methods, Fundamental Theories of Physics, vol. 57. Kluwer academic publishers, Dordrecht (1993)
  20.Vértesi, T., Bene, E.: Two-qubit Bell inequality for which positive operator-valued measurements are relevant. Phys. Rev. A 82(6), 062115 (2010)CrossRef
  
• 作者单位：Mojtaba Aliakbarzadeh (16)
  Kirsty Kitto (16)
  
  16. Queensland University of Technology, Brisbane, 4000, Australia
  
• 丛书名：Quantum Interaction
• ISBN：978-3-319-28675-4
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349

文摘

Much of the work currently occurring in the field of Quantum Interaction (QI) relies upon Projective Measurement. This is perhaps not optimal, cognitive states are not nearly as well behaved as standard quantum mechanical systems; they exhibit violations of repeatability, and the operators that we use to describe measurements do not appear to be naturally orthogonal in cognitive systems. Here we attempt to map the formalism of Positive Operator Valued Measure (POVM) theory into the domain of semantic memory, showing how it might be used to construct Bell-type inequalities.