Advanced tools and concepts for quantum cognition: A tutorial

This tutorial is intended to provide an introduction to some advanced tools and concepts needed to construct more realistic quantum models of cognition and decision. The aim is to cover, in a format suitable for researchers with some limited exposure to quantum models of cognition, the ideas of density matrices, POVM type measurements and open system dynamics. The central theme we explore is how we might introduce noise into our quantum models, and the effect this has on model behavior. These important ideas are likely to be very useful for constructing more realistic cognitive models, but they are generally not covered by introductory accounts of quantum theory. We hope that this tutorial will help to introduce these tools to other researchers interested in constructing quantum models of cognition.

[1]  Shmuel Zamir,et al.  Type Indeterminacy-A Model of the KT-man ( Kahneman Tversky ) , 2003 .

[2]  Richard M. Shiffrin,et al.  Context effects produced by question orders reveal quantum nature of human judgments , 2014, Proceedings of the National Academy of Sciences.

[3]  Honors Thesis,et al.  AN AXIOMATIC FORMULATION OF QUANTUM MECHANICS , 2009 .

[4]  Ehtibar N. Dzhafarov,et al.  Quantum Models for Psychological Measurements: An Unsolved Problem , 2014, PloS one.

[5]  Emmanuel M Pothos,et al.  Zeno's paradox in decision-making , 2016, Proceedings of the Royal Society B: Biological Sciences.

[6]  Paz,et al.  Quantum Brownian motion in a general environment: Exact master equation with nonlocal dissipation and colored noise. , 1992, Physical review. D, Particles and fields.

[7]  Jennifer S Trueblood,et al.  A quantum geometric model of similarity. , 2013, Psychological review.

[8]  Jennifer Trueblood,et al.  A Quantum Probability Account of Order Effects in Inference , 2011, Cogn. Sci..

[9]  J. Tenenbaum,et al.  Special issue on “Probabilistic models of cognition , 2022 .

[10]  Jerome R Busemeyer,et al.  Can quantum probability provide a new direction for cognitive modeling? , 2013, The Behavioral and brain sciences.

[11]  Emmanuel M. Pothos,et al.  A Quantum Probability Perspective on Borderline Vagueness , 2013, Top. Cogn. Sci..

[12]  F. Witte,et al.  Book Review: Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets. Prof. Dr. Hagen Kleinert, 3rd extended edition, World Scientific Publishing, Singapore , 2003 .

[13]  Yoshiharu Tanaka,et al.  Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology , 2015, Foundations of Physics.

[14]  David A. Clifton,et al.  A Probabilistic Framework for M-Health , 2013 .

[15]  G. Lindblad On the generators of quantum dynamical semigroups , 1976 .

[16]  Andrei Khrennikov,et al.  Quantum model for psychological measurements: from the projection postulate to interference of mental observables represented as positive operator valued measures , 2014, 1405.1269.

[17]  Shmuel Zamir,et al.  Type Indeterminacy: A Model for the KT(Kahneman-Tversky)-Man , 2006, physics/0604166.

[18]  Diederik Aerts,et al.  Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought , 2012, Top. Cogn. Sci..

[19]  Diederik Aerts,et al.  Quantum Structure in Cognition , 2008, 0805.3850.

[20]  A. Leggett,et al.  Path integral approach to quantum Brownian motion , 1983 .

[21]  Edwin T. Jaynes Prior Probabilities , 2010, Encyclopedia of Machine Learning.

[22]  Rodolfo Gambini,et al.  An axiomatic formulation of the Montevideo interpretation of quantum mechanics , 2010, 1002.4209.

[23]  Masanori Ohya,et al.  Quantum-Like Model for Decision Making Process in Two Players Game , 2011 .

[24]  Yoshiharu Tanaka,et al.  Dynamics of Entropy in Quantum-like Model of Decision Making. , 2011 .

[25]  Emmanuel M Pothos,et al.  Challenging the classical notion of time in cognition: a quantum perspective , 2014, Proceedings of the Royal Society B: Biological Sciences.

[26]  Emmanuel M. Pothos,et al.  Progress and current challenges with the quantum similarity model , 2015, Front. Psychol..

[27]  Stanislaw Kryszewski,et al.  Master equation - tutorial approach , 2008, 0801.1757.

[28]  Laurianne Sitbon,et al.  A probabilistic framework for analysing the compositionality of conceptual combinations , 2013, ArXiv.

[29]  Peter D. Kvam,et al.  Interference effects of choice on confidence: Quantum characteristics of evidence accumulation , 2015, Proceedings of the National Academy of Sciences.

[30]  A. Cabello Bibliographic guide to the foundations of quantum mechanics and quantum information , 2000, quant-ph/0012089.

[31]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[32]  J. Kleijnen,et al.  Context Effects , 2003 .

[33]  J. Busemeyer,et al.  A quantum probability explanation for violations of ‘rational’ decision theory , 2009, Proceedings of the Royal Society B: Biological Sciences.

[34]  Marian Grabowski,et al.  Operational Quantum Physics , 2001 .

[35]  I. Tietje,et al.  Attosecond neutron scattering from open quantum systems: Entanglement and decoherence phenomena of protons in condensed matter and molecules , 2010 .

[36]  Yoshiharu Tanaka,et al.  Quantum-like dynamics of decision-making , 2012 .

[37]  Yoshiharu Tanaka,et al.  Quantum-like generalization of the Bayesian updating scheme for objective and subjective mental uncertainties , 2012 .

[38]  Asher Peres,et al.  Quantum Theory: Concepts and Methods , 1994 .

[39]  J. J. Halliwell,et al.  How the quantum universe became classical , 2005 .

[40]  Jerome R. Busemeyer,et al.  A Quantum Question Order Model Supported by Empirical Tests of an A Priori and Precise Prediction , 2013, Top. Cogn. Sci..

[41]  H. Atmanspacher,et al.  Order Effects in Sequential Measurements of Non-Commuting Psychological Observables , 2012, 1201.4685.

[42]  Ismael Martínez-Martínez,et al.  A quantum-like model for complementarity of preferences and beliefs in dilemma games , 2017 .

[43]  Ting Yu Decoherence and localization in quantum two-level systems , 1996 .

[44]  Emmanuel M. Pothos,et al.  decision theory A quantum probability explanation for violations of ' rational ' Supplementary data tml , 2009 .

[45]  Francesco Petruccione,et al.  The Theory of Open Quantum Systems , 2002 .

[46]  Emmanuel M. Pothos,et al.  Sometimes it does hurt to ask: The constructive role of articulating impressions , 2014, Cognition.

[47]  Harald Atmanspacher,et al.  A proposed test of temporal nonlocality in bistable perception , 2010 .

[48]  Jerome R. Busemeyer,et al.  A Comparison of the Belief-Adjustment Model and the Quantum Inference Model as Explanations of Order Effects in Human Inference , 2010 .

[49]  W. Zurek The Environment, Decoherence and the Transition from Quantum to Classical , 1991 .

[50]  Yoshiharu Tanaka,et al.  Quantum-like model of brain's functioning: decision making from decoherence. , 2011, Journal of theoretical biology.

[51]  Jerome R. Busemeyer,et al.  Quantum Models of Cognition and Decision , 2012 .

[52]  Andrei Khrennikov,et al.  Ubiquitous Quantum Structure: From Psychology to Finance , 2010 .

[53]  Harald Atmanspacher,et al.  The Potential of Using Quantum Theory to Build Models of Cognition , 2013, Top. Cogn. Sci..

[54]  H. Kleinert Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets , 2006 .

[55]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[56]  Didier Sornette,et al.  Decision theory with prospect interference and entanglement , 2011, ArXiv.

[57]  Jonathan J. Halliwell Two derivations of the master equation of quantum Brownian motion , 2007 .

[58]  James M. Yearsley,et al.  Quantum cognition and decision theories: A tutorial , 2016 .