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2016 | OriginalPaper | Buchkapitel

Applying POVM to Model Non-orthogonality in Quantum Cognition

verfasst von : Mojtaba Aliakbarzadeh, Kirsty Kitto

Erschienen in: Quantum Interaction

Verlag: Springer International Publishing

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Abstract

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.

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Literatur
1.
Zurück zum Zitat Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of bell inequalities in the macroworld. Found. Phys. 30(9), 1387–1414 (2000)MathSciNetCrossRef Aerts, D., Aerts, S., Broekaert, J., Gabora, L.: The violation of bell inequalities in the macroworld. Found. Phys. 30(9), 1387–1414 (2000)MathSciNetCrossRef
3.
Zurück zum Zitat Ballentine, L.: Quantum Mechanics: A Modern Development. World Scientific, Singapore (1998)MATHCrossRef Ballentine, L.: Quantum Mechanics: A Modern Development. World Scientific, Singapore (1998)MATHCrossRef
4.
Zurück zum Zitat 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)MathSciNetCrossRef 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)MathSciNetCrossRef
5.
Zurück zum Zitat 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)MATHMathSciNetCrossRef 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)MATHMathSciNetCrossRef
6.
Zurück zum Zitat 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) 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)
8.
Zurück zum Zitat Dzhafarov, E., Kujala, J.: Selectivity in probabilistic causality: where psychology runs into quantum physics. J. Math. Psychol. 56, 54–63 (2012)MATHMathSciNetCrossRef Dzhafarov, E., Kujala, J.: Selectivity in probabilistic causality: where psychology runs into quantum physics. J. Math. Psychol. 56, 54–63 (2012)MATHMathSciNetCrossRef
9.
Zurück zum Zitat 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 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
12.
Zurück zum Zitat 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 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.
Zurück zum Zitat Kitto, K., Ramm, B., Sitbon, L., Bruza, P.D.: Quantum theory beyond the physical: information in context. Axiomathes 21(2), 331–345 (2011)CrossRef Kitto, K., Ramm, B., Sitbon, L., Bruza, P.D.: Quantum theory beyond the physical: information in context. Axiomathes 21(2), 331–345 (2011)CrossRef
15.
Zurück zum Zitat Maudlin, T.: Quantum Non-locality and Relativity: Metaphysical Intimations of Modern Physics, Aristotelian Society Series, vol. 13. Blackwell publishers limited, Oxford, UK (1994) Maudlin, T.: Quantum Non-locality and Relativity: Metaphysical Intimations of Modern Physics, Aristotelian Society Series, vol. 13. Blackwell publishers limited, Oxford, UK (1994)
17.
Zurück zum Zitat 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 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.
Zurück zum Zitat Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
19.
Zurück zum Zitat Peres, A.: Quantum Theory: Concepts and Methods, Fundamental Theories of Physics, vol. 57. Kluwer academic publishers, Dordrecht (1993) Peres, A.: Quantum Theory: Concepts and Methods, Fundamental Theories of Physics, vol. 57. Kluwer academic publishers, Dordrecht (1993)
20.
Zurück zum Zitat Vértesi, T., Bene, E.: Two-qubit Bell inequality for which positive operator-valued measurements are relevant. Phys. Rev. A 82(6), 062115 (2010)CrossRef Vértesi, T., Bene, E.: Two-qubit Bell inequality for which positive operator-valued measurements are relevant. Phys. Rev. A 82(6), 062115 (2010)CrossRef
Metadaten
Titel
Applying POVM to Model Non-orthogonality in Quantum Cognition
verfasst von
Mojtaba Aliakbarzadeh
Kirsty Kitto
Copyright-Jahr
2016
DOI
https://doi.org/10.1007/978-3-319-28675-4_22

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