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Über dieses Buch

This book constitutes the refereed proceedings of the 6th International Symposium on Quantum Interaction, QI 2012, held in Paris in June 2012. The 21 revised full papers presented were carefully reviewed and selected from 32 submissions. The papers cover various topics on quantum interaction.



The Quantum Inspired Modelling of Changing Attitudes and Self-organising Societies

We utilise the quantum decision models, now well-developed in the QI community, to create a higher order social decision making model. A simple Agent Based Model (ABM) of a society of agents with changing attitudes towards a social issue is presented, where the private attitudes of individuals in the system are represented using a geometric structure inspired by quantum theory. We track the changing attitudes of the members of that society, and their resulting propensities to act, or not, in a given social context. A number of new issues surrounding this “scaling up” of quantum decision theories are discussed, as well as new directions and opportunities.

Kirsty Kitto, Fabio Boschetti, Peter Bruza

On Least Action Principles for Discrete Quantum Scales

We consider variational problems where the velocity depends on a scale. After recalling the fundamental principles that lead to classical and quantum mechanics, we study the dynamics obtained by replacing the velocity by some physical observable at a given scale into the expression of the Lagrangian function. Then, discrete Euler-Lagrange and Hamilton-Jacobi equations are derived for a continuous model that incorporates a real-valued discrete velocity. We also examine the paradigm for complex-valued discrete velocity, inspired by the scale relativity of Nottale. We present also rigorous definitions and preliminary results in this direction.

François Dubois, Isabelle Greff, Thomas Hélie

Real, Complex, and Binary Semantic Vectors

This paper presents a combined structure for using real, complex, and binary valued vectors for semantic representation. The theory, implementation, and application of this structure are all significant.

For the theory underlying quantum interaction, it is important to develop a core set of mathematical operators that describe systems of information, just as core mathematical operators in quantum mechanics are used to describe the behavior of physical systems. The system described in this paper enables us to compare more traditional quantum mechanical models (which use complex state vectors), alongside more generalized quantum models that use real and binary vectors.

The implementation of such a system presents fundamental computational challenges. For large and sometimes sparse datasets, the demands on time and space are different for real, complex, and binary vectors. To accommodate these demands, the Semantic Vectors package has been carefully adapted and can now switch between different number types comparatively seamlessly.

This paper describes the key abstract operations in our semantic vector models, and describes the implementations for real, complex, and binary vectors. We also discuss some of the key questions that arise in the field of quantum interaction and informatics, explaining how the wide availability of modelling options for different number fields will help to investigate some of these questions.

Dominic Widdows, Trevor Cohen

The Guppy Effect as Interference

People use conjunctions and disjunctions of concepts in ways that violate the rules of classical logic, such as the law of compositionality. Specifically, they overextend conjunctions of concepts, a phenomenon referred to as the Guppy Effect. We build on previous efforts to develop a quantum model [1,2,3], that explains the Guppy Effect in terms of interference. Using a well-studied data set with 16 exemplars that exhibit the Guppy Effect, we developed a 17-dimensional complex Hilbert space

${\cal H}$

that models the data and demonstrates the relationship between overextension and interference. We view the interference effect as, not a logical fallacy on the conjunction, but a signal that out of the two constituent concepts, a


concept has emerged.

Diederik Aerts, Jan Broekaert, Liane Gabora, Tomas Veloz

A Quantum Model for the Ellsberg and Machina Paradoxes




Machina paradoxes

reveal that

expected utility theory

is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but none of them provides a satisfactory solution of the Machina paradox. In this paper we elaborate a quantum model in Hilbert space describing the Ellsberg situation and also the Machina situation, and show that we can model the specific aspect of the Machina situation that is unable to be modeled within the existing generalizations of expected utility.

Diederik Aerts, Sandro Sozzo, Jocelyn Tapia

A Quantum-Like Model of Escherichia coli’s Metabolism Based on Adaptive Dynamics

Recently it is pointed out that there exists the experimental data in

Escherichia coli

’s metabolism which violate the law of total probability in classical probability. In this report, we propose a model which describes such phenomenon based on adaptive dynamics.

Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya, Yoshiharu Tanaka, Ichiro Yamato

Fractals, Dissipation and Coherent States

Self-similarity properties of fractal structures, including the logarithmic spiral, are related to quantum dissipative dynamics, generalized squeezed coherent states and noncommutative geometry in the plane. The rôle played by the fractal Hamiltonian which actually turns out to be the fractal free energy is discussed. Time evolution characterized by the breakdown of time-reversal symmetry is controlled by the entropy. Coherent boson condensation induced by the generators of the coherent states is shown to control the formation of fractals. Vice-versa, coherent generalized states are recognized to possess self-similar fractal structure. The global nature of fractals appears to emerge from irreversible coherent local deformation processes.

Giuseppe Vitiello

Hierarchical Bayesian Estimation of Quantum Decision Model Parameters

Quantum decision models have been recently proposed to account for findings that have resisted explanation by traditional decision theories. This paper compares quantum versus Markov models of decision making for explaining a puzzling empirical finding from human decision making called dynamic inconsistency – that is the failure of decision makers to carry out their planned decisions. A large data set that empirically investigated dynamic inconsistency was used to quantitatively evaluate the quantum and Markov models. In this application, the quantum model reduces to the Markov model when one of the parameters is set to zero. The parameters of the quantum model were estimated using Hierarchical Bayesian estimation. The distribution of the key quantum parameter was clearly located in the quantum regime and far below zero as predicted by the Markov model. These results provide further support for quantum models as compared to the traditional models of decision making.

Jerome R. Busemeyer, Zheng Wang, Jennifer S. Trueblood

Many Paths Lead to Discovery: Analogical Retrieval of Cancer Therapies

This paper addresses the issue of analogical inference, and its potential role as the mediator of new therapeutic discoveries, by using disjunction operators based on quantum connectives to combine many potential reasoning pathways into a single search expression. In it, we extend our previous work in which we developed an approach to analogical retrieval using the Predication-based Semantic Indexing (PSI) model, which encodes both concepts and the relationships between them in high-dimensional vector space. As in our previous work, we leverage the ability of PSI to infer predicate pathways connecting two example concepts, in this case comprising of known therapeutic relationships. For example, given that

drug x


disease z

, we might infer the predicate pathway

drug x


gene y


disease z

, and use this pathway to search for drugs related to another disease in similar ways. As biological systems tend to be characterized by networks of relationships, we evaluate the ability of quantum-inspired operators to mediate inference and retrieval across multiple relations, by testing the ability of different approaches to recover known therapeutic relationships. In addition, we introduce a novel complex vector based implementation of PSI, based on Plate’s Circular Holographic Reduced Representations, which we utilize for all experiments in addition to the binary vector based approach we have applied in our previous research.

Trevor Cohen, Dominic Widdows, Lance De Vine, Roger Schvaneveldt, Thomas C. Rindflesch

Emergence and Instability of Individual Identity

The Type Indeterminacy model is a theoretical framework that uses some elements of quantum formalism to model the constructive preference perspective suggested by Kahneman and Tversky. In a dynamic decision context, type indeterminacy provides a framework for investigating the emergence and evolution of identity as the outcome of the interaction between multiple potential selves (eigentypes). We define a dynamic game among the selves with individual identity (preferences) as the state variable. In the Markov perfect equililibrium of the game, identity arises as ”a relational property” that does not pre-exist the decision context. The approach allows to characterize generic personality types and derive some comparitive static results.

Ariane Lambert-Mogiliansky, Jerome R. Busemeyer

Entanglement of Conceptual Entities in Quantum Model Theory (QMod)

We have recently elaborated

Quantum Model Theory



) 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.

Diederik Aerts, Sandro Sozzo

Quantum Model Theory (QMod): Modeling Contextual Emergent Entangled Interfering Entities

In this paper we present

Quantum Model Theory



), a theory we developed to model entities that entail the typical quantum effects of










. The aim of


is to put forward a theoretical framework that is more general than standard quantum mechanics, in the sense that, for its complex version it only uses this quantum calculus locally, i.e. for each context corresponding to a measurement, and for its real version it does not need the property of ‘linearity of the set of states’ to model the quantum effect. In this sense,


is a generalization of quantum mechanics, similar to how the general relativity manifold mathematical formalism is a generalization of special relativity. We prove by means of a representation theorem that


can be used for any entity entailing the typical quantum effects mentioned above. Some examples of application of QMod in concept theory and macroscopic physics are also considered.

Diederik Aerts, Sandro Sozzo

Quantum-Like Representation of Irrational Inference

In this paper we develop a general quantum-like representation of decision making. Here

quantum-like representation

is based on linear algebra, the von Neumann-Lüders projection postulate, Born’s rule, and the quantum representation of the state space of a composite system by the tensor product. Our approach generalizes in a natural way the classical Bayesian inference and explains irrational (non-Bayesian) inference biased by psychological factors. For the mathematical description of irrational inference, we use the

lifting map

, which is important concept to discuss a general quantum dynamics called adaptive dynamics.

Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya, Yoshiharu Tanaka

Type Indeterminacy in Privacy Decisions: The Privacy Paradox Revisited

The paper at hand aims to provide a rational explanation of why people generously give away personal data while at the same time being highly concerned about their privacy. For many years, research has come up with attempts to untangle the privacy paradox. We provide a thorough literature review on privacy decisions in socio-economic scenarios and identify explanatory gaps. To explain paradoxical behavior in privacy decision making we illuminate (1) generous data disclosure and (2) high valuation of privacy as two non-commuting observations of incompatible preferences (types). Abstract risk awareness of privacy threats and concrete privacy decisions are not interchangeable, i.e. disclosing personal data prior to becoming aware of privacy risks does not equal the raising of risk awareness before revealing personal information. Privacy decisions do not commute as subjects may alter their preferences indeterminately, i.e. at the time an actual decision is made, in response to discomfort arising from conflicting preferences.

Christian Flender, Günter Müller

Adaptive Dynamics and Its Application to Context Dependent Systems Breaking the Classical Probability Law

There exist several phenomena (systems) breaking the classical probability laws. In this report, we present a new mathematical formula to compute the probability in those context dependent systems by using the concepts of the adaptive dynamics and the lifting.

Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya, Yoshiharu Tanaka, Ichiro Yamato

Modelling Word Activation in Semantic Networks: Three Scaled Entanglement Models Compared

Modelling how a word is activated in human memory is an important requirement for determining the probability of recall of a word in an extra-list cueing experiment. Previous research assumed a quantum-like model in which the semantic network was modelled as entangled qubits, however the level of activation was clearly being overestimated. This paper explores three variations of this model, each of which are distinguished by a scaling factor designed to compensate the overestimation.

David Galea, Peter Bruza, Kirsty Kitto, Douglas Nelson

Quantum Entanglement and the Issue of Selective Influences in Psychology: An Overview

Similar formalisms have been independently developed in psychology, to deal with the issue of selective influences (deciding which of several experimental manipulations selectively influences each of several, generally non-independent, response variables), and in quantum mechanics (QM), to deal with the EPR entanglement phenomena (deciding whether an EPR experiment allows for a “classical” account). The parallels between these problems are established by observing that any two noncommuting measurements in QM are mutually exclusive and can therefore be treated as analogs of different values of one and the same input. Both problems reduce to that of the existence of a jointly distributed system of random variables, one variable for every value of every input (in psychology) or every measurement on every particle involved (in an EPR experiment). We overview three classes of necessary conditions (some of them also sufficient under additional constraints) for the existence of such joint distributions.

Ehtibar N. Dzhafarov, Janne V. Kujala

Quantum-Like Behavior of Classical Systems

Bohmian mechanics is an example for a classical theory with a (Newtonian) ontology which reproduces all features of quantum mechanics. It is often used as a “classical” formulation of quantum mechanics, but in this article we invert the argument: Bohmian mechanics proves that there are classical systems which can show a quantum-like behavior; in particular, such models are able to explain non-classical probabilities. We analyze the general structure of Bohmian-type models and argue, that neural processes related to the correlates of mental states are likely to follow a dynamics which is similar to this class of models. Therefore, it may not be too surprising that cognitive phenomena under certain circumstances show a quantum-like behavior.

Thomas Filk

Connecting the Dots: Mass, Energy, Word Meaning, and Particle-Wave Duality

With insight from linguistics that degrees of text cohesion are similar to forces in physics, and the frequent use of the energy concept in text categorization by machine learning, we consider the applicability of particle-wave duality to semantic content inherent in index terms. Wave-like interpretations go back to the regional nature of such content, utilizing functions for its representation, whereas content as a particle can be conveniently modelled by position vectors. Interestingly, wave packets behave like particles, lending credibility to the duality hypothesis. We show in a classical mechanics framework how metaphorical term mass can be computed.

Sándor Darányi, Peter Wittek

Indiscernability and Mean Field, a Base of Quantum Interaction

We study the convergence of the Schrödinger equation, when the Planck constant tends to 0. Our analysis leads us to introduce non-discerned particles in classical mechanics and discerned particles in quantum mechanics. These non-discerned particles in classical mechanics correspond to an action and a density which verify the statistical Hamilton-Jacobi equations. The indiscernability of classical particles provides a very simple and natural explanation to the Gibbs paradox. We then consider the case of a large number of identical non-discerned interacting particles modeled by a mean field. In classical mechanics these particles satisfy the mean field Hamilton-Jacobi equations. We show how the analysis of non-discerned particles in classical mechanics can be fruitfully applied to some other fields. In economics, we show that the theory of mean field games, where non-discerned agents are considered interacting with one another, is the analogue of mean field Hamilton-Jacobi equations.

Michel Gondran, Sébastien Lepaul

Social-Psychological Harmonic Oscillators in the Self-regulation of Organizations and Systems

We propose

ab initio

the existence of social-psychological harmonic oscillators (SPHO) acting computationally in the minds of an intelligent audience that a self-regulated collective exploits to solve problems, resolve complex issues, or entertain itself. Using computational intelligence, our ultimate goal is to self-regulate systems composed of humans, machines and robots. We conclude in an overview that self-regulation, characterized by our solution of the nonlinear tradeoffs between Fourier pairs of Gaussian distributions, affects decision-making differently for organizations and systems: When set inside of a democracy to solve well-defined problems, optimum performance requires command decision-making along with maximum cooperation among an organization’s multitaskers (few challenges maximize oscillations); but, to solve ill-defined problems across a system requires maximum competition among participants and organizations (challenges minimize oscillations).

William F. Lawless, Donald A. Sofge


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