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Quantum Interaction

10th International Conference, QI 2016, San Francisco, CA, USA, July 20-22, 2016, Revised Selected Papers

herausgegeben von: Jose Acacio de Barros, Bob Coecke, Emmanuel Pothos

Verlag: Springer International Publishing

Buchreihe : Lecture Notes in Computer Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Quantum Interaction, QI 2016, held in San Francisco, CA, USA, in July 2016.
The 21 papers presented in this book were carefully reviewed and selected from 39 submissions. The papers address topics such as: Fundamentals; Quantum Cognition; Language and Applications; Contextuality and Foundations of Probability; and Quantum-Like Measurements.

Inhaltsverzeichnis

Frontmatter

Fundamentals

Frontmatter

Interpretations of QM with Applications for Formal Epistemology

Abstract

Associated with the Copenhagen school, the External Observation View of quantum mechanics depicted a quantum state as evolving deterministically, but with interruptions when ‘collapsed’ by measurement interactions. I will point to an analogy with the doxastic state studied in epistemology, and show that this analogy suggests an application of the quantum mechanical formalism that leads to a proof of one solution of a central problem in formal epistemology. I will end with some critical remarks.

Bas C. van Fraassen

Contextuality-by-Default 2.0: Systems with Binary Random Variables

Abstract

The paper outlines a new development in the Contextuality-by-Default theory as applied to finite systems of binary random variables. The logic and principles of the original theory remain unchanged, but the definition of contextuality of a system of random variables is now based on multimaximal rather than maximal couplings of the variables that measure the same property in different contexts: a system is considered noncontextual if these multimaximal couplings are compatible with the distributions of the random variables sharing contexts. A multimaximal coupling is one that is a maximal coupling of any subset (equivalently, of any pair) of the random variables being coupled. Arguments are presented for why this modified theory is a superior generalization of the traditional understanding of contextuality in quantum mechanics. The modified theory coincides with the previous version in the important case of cyclic systems, which include the systems whose contextuality was most intensively studied in quantum physics and behavioral sciences.

Ehtibar N. Dzhafarov, Janne V. Kujala

Probabilistic Nature of a Field with Time as a Dynamical Variable

Abstract

Taking time as a dynamical variable, we study a wave with 4-vector amplitude that has vibrations of matter in space and time. By analyzing its Hamiltonian density equation, we find that the system is quantized. It obeys the Klein-Gordon equation and thus also the Schrödinger equation. Only a probability can be assigned for the detection of a particle. This quantized field has physical structures that resemble a zero-spin quantum field. The possibility to apply our formalism outside quantum physics is briefly discussed.

Hou Y. Yau

Quantum Cognition

Frontmatter

Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition: Metaphors of Two and Three Slit Experiments

Abstract

Analogy between the two slit experiment in quantum mechanics (QM) and the disjunction effect in psychology led to fruitful applications of the mathematical formalism of quantum probability to cognitive psychology. These quantum-like studies demonstrated that quantum probability (QP) matches better with the experimental statistical data than classical probability (CP). Similar conclusion can be derived from comparing QP and CP models for a variety of other cognitive-psychological effects, e.g., the order effect. However, one may wonder whether QP covers completely cognitive-psychological phenomena or cognition exhibits even more exotic probabilistic features and we have to use probabilistic models with even higher degree of nonclassicality than quantum probability. It is surprising that already a cognitive analog of the triple slit experiment in QM can be used to check this problem.

Irina Basieva, Andrei Khrennikov

Contextuality in the Integrated Information Theory

Abstract

Integrated Information Theory (IIT) is one of the most influential theories of consciousness, mainly due to its claim of mathematically formalizing consciousness in a measurable way. However, the theory, as it is formulated, does not account for contextual observations that are crucial for understanding consciousness. Here we put forth three possible difficulties for its current version, which could be interpreted as a trilemma. Either consciousness is contextual or not. If contextual, either IIT needs revisions to its axioms to include contextuality, or it is inconsistent. If consciousness is not contextual, then IIT faces an empirical challenge. Therefore, we argue that IIT in its current version is inadequate.

J. Acacio de Barros, Carlos Montemayor, Leonardo P. G. De Assis

Is Stress Quantum-Like?

Abstract

In this paper we examine two well-controlled experiments where order effects were shown under stress. We show that for only one of those experiments the QQ equality of Wang and Busemeyer [21] seems to be fairly satisfied (under independence assumptions). Since the experiment satisfying QQ measures physiological variables, this may suggest that quantum order effect outside human judgment models.

J. Acacio de Barros, Leonardo Guimarães De Assis, Petr Bob

Quantum Cognition Beyond Hilbert Space: Fundamentals and Applications

Abstract

The ‘quantum cognition’ paradigm was recently challenged by its proven impossibility to simultaneously model ‘question order effects’ and ‘response replicability’. In the present article we describe sequential dichotomic measurements within an operational and realistic framework for human cognition, and represent them in a quantum-like ‘extended Bloch representation’, where the Born rule of quantum probability does not necessarily hold. We then apply this mathematical framework to successfully model question order effects, response replicability and unpacking effects, thus opening the way toward ‘quantum cognition beyond Hilbert space’.

Diederik Aerts, Lyneth Beltran, Massimiliano Sassoli de Bianchi, Sandro Sozzo, Tomas Veloz

Toward a Gauge Theory of Musical Forces

Abstract

How well does a given pitch fit into a tonal scale or key, being either a major or minor key? This question addresses the well-known phenomenon of tonal attraction in music psychology. Metaphorically, tonal attraction is often described in terms of attracting and repelling forces that are exerted upon a probe tone of a scale. In modern physics, forces are related to gauge fields expressing fundamental symmetries of a theory. In this study we address the intriguing relationship between musical symmetries and gauge forces in the framework of quantum cognition.

Peter beim Graben, Reinhard Blutner

Language and Applications

Frontmatter

Quantum Bootstrap Aggregation

Abstract

We set out a strategy for quantizing attribute bootstrap aggregation to enable variance-resilient quantum machine learning. To do so, we utilise the linear decomposability of decision boundary parameters in the Rebentrost et al. Support Vector Machine to guarantee that stochastic measurement of the output quantum state will give rise to an ensemble decision without destroying the superposition over projective feature subsets induced within the chosen SVM implementation. We achieve a linear performance advantage, O(d), in addition to the existing O(log(n)) advantages of quantization as applied to Support Vector Machines. The approach extends to any form of quantum learning giving rise to linear decision boundaries.

David Windridge, Rajagopal Nagarajan

Categorical Compositional Cognition

Abstract

We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic problems with ICS such as the fact that representations inhabit an unbounded space and that sentences with differing tree structures cannot be directly compared. We do so in a way that makes the most of the grammatical structure available, in contrast to strategies like circular convolution. Using the CatCo model also allows us to make use of tools developed for CatCo such as the representation of ambiguity and logical reasoning via density matrices, structural meanings for words such as relative pronouns, and addressing over- and under-extension, all of which are present in cognitive processes. Moreover the CatCog framework is sufficiently flexible to allow for entirely different representations of meaning, such as conceptual spaces. Interestingly, since the CatCo model was largely inspired by categorical quantum mechanics, so is CatCog.

Yaared Al-Mehairi, Bob Coecke, Martha Lewis

Graded Vector Representations of Immunoglobulins Produced in Response to West Nile Virus

Abstract

Semantic vector models generate high-dimensional vector representations of words from their occurrence statistics across large corpora of electronic text. In these models, an occurrence of a word or number is treated as a discrete event, including numerical measurements of continuous properties. Furthermore, the sequence in which words occur is often ignored. In earlier work we have developed approaches to address these limitations, using graded demarcator vectors to represent measured distances in high-dimensional space. This permits incorporation of continuous properties, such as the position of a character within a term or a year of birth, into semantic vector models. In this paper we extend this work by developing a novel representational approach for protein sequences, in which both the positions and the properties of the amino acid components of protein sequences are represented using graded vectors. Evaluation on a set of around 100,000 immunoglobulin receptor sequences derived from subjects recently infected with West Nile Virus (WNV) suggests that encoding positions and properties using graded vectors increases the similarity between immunoglobulin receptor sequences produced by cells from ancestral lines known to have developed in response to WNV, relative to those from other cell lines.

Trevor Cohen, Dominic Widdows, Jason A. Vander Heiden, Namita T. Gupta, Steven H. Kleinstein

Contextuality and Foundations of Probability

Frontmatter

Testing Contextuality in Cyclic Psychophysical Systems of High Ranks

Abstract

Contextuality-by-Default (CbD) is a mathematical framework for understanding the role of context in systems with deterministic inputs and random outputs. A necessary and sufficient condition for contextuality was derived for cyclic systems with binary outcomes. In quantum physics, the cyclic systems of ranks \(n=\) 5, 4, and 3 are known as systems of Klyachko-type, EPR-Bell-type, and Leggett-Garg-type, respectively. In earlier publications, we examined data collected in various behavioral and social scenarios, from polls of public opinion to our own experiments with psychophysical matching. No evidence of contextuality was found in these data sets. However, those studies were confined to cyclic systems of lower ranks (\(n\le 4\)). In this paper, contextuality of higher ranks (\(n=6,8\)) was tested on our data with psychophysical matching, and again, no contextuality was found. This may indicate that many if not all of the seemingly contextual effects observed in behavioral sciences are merely violations of consistent connectedness (selectiveness of influences).

Ru Zhang, Ehtibar N. Dzhafarov

Probabilistic Programs: Contextuality and Relational Database Theory

Abstract

[6] have introduced a contextual probability theory called Contextuality-by-Default (C-b-D) which is based on three principles. The first of these principles states that each random variable should be automatically labeled by all condition under which it is recorded. The aim of this article is to relate this principle to block structured computer programming languages where variables are declared local to a construct called a “scope”. In this way a variable declared in two scopes can be safely overloaded meaning that they can have the same label but preserve two distinct identities without the need for the modeller to label each variable in each condition as advocated by C-b-D. A core issue addressed is how to construct a single probabilistic model from the various interim probability distributions returned by each syntactic scope. For this purpose, a probabilistic variant of the natural join operator of relational algebra is used to “glue” together interim distributions into a single distribution. The semantics of this join operator are related to contextual semantics [1].

P. D. Bruza, S. Abramsky

On Peculiar Relations Between Measurement Incompatibility and Contextuality

Abstract

We use algorithmic information to define co-measurability of observables and investigate its relation to the phenomenon of quantum contextuality.

Dagomir Kaszlikowski, Paweł Kurzyński

Exploration of Contextuality in a Psychophysical Double-Detection Experiment

Abstract

The Contextuality-by-Default (CbD) theory allows one to separate contextuality from context-dependent errors and violations of selective influences (aka “no-signaling” or “no-disturbance” principles). This makes the theory especially applicable to behavioral systems, where violations of selective influences are ubiquitous. For cyclic systems with binary random variables, CbD provides necessary and sufficient conditions for noncontextuality, and these conditions are known to be breached in certain quantum systems. We apply the theory of cyclic systems to a psychophysical double-detection experiment, in which observers were asked to determine presence or absence of a signal property in each of two simultaneously presented stimuli. The results, as in all other behavioral and social systems previously analyzed, indicate lack of contextuality. The role of context in double-detection is confined to lack of selectiveness: the distribution of responses to one of the stimuli is influenced by the state of the other stimulus.

Víctor H. Cervantes, Ehtibar N. Dzhafarov

On the Interpretation of Probabilities in Generalized Probabilistic Models

Abstract

We discuss generalized probabilistic models for which states not necessarily obey Kolmogorov’s axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.

Federico Holik, Sebastian Fortin, Gustavo Bosyk, Angelo Plastino

An Introduction to Symmetric Inflated Probabilities

Abstract

Traditionally, probability is treated as a function that takes values in the interval [0, 1]. All conventional interpretations of probability support this assumption, while all popular formal descriptions, e.g., axioms for probability, such as Kolmogorov’s axioms, canonize this premise. However, researchers found that negative, as well as larger than 1 probabilities could be a useful tool in physics. Some even assert that probabilities that can be negative, larger than 1 or less than −1 are necessary for physics. Here we develop an axiomatic system for such probabilities, which are called symmetric inflated probabilities and reflect interaction of particles and antiparticles, and study their properties.

Mark Burgin

Quantum-Like Measurements

Frontmatter

A First Attempt at Ordinal Projective Measurement

Abstract

To our knowledge, all applications of the quantum framework in social sciences are used to model measurements done on a discrete nominal scale. However, especially in cognition, experiments often produce data on an ordinal scale, which implies some internal structure between the possible outcomes. Since there are no ordinal scales in physics, orthodox projection-valued measurement (PVM) lacks the tools and methods to deal with these ordinal scales. Here, we sketch out an attempt to incorporate the ordinal structure of outcomes into the subspaces representing these outcomes. This will also allow us to reduce the dimensionality of the resulting Hilbert spaces, as these often become too high in more complex quantum-like models. To do so, we loosen restrictions placed upon the PVM (and even POVM) framework. We discuss the two major consequences of this generalization: scaling and the loss of repeatability. We also present two applications of this approach, one in game theory and one concerning Likert scales.

Jacob Denolf

Eigenlogic: A Quantum View for Multiple-Valued and Fuzzy Systems

Abstract

We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the respective eigenvectors. For binary logic using the truth values \(\{0,1\}\) logical observables are pairwise commuting projectors. For the truth values \(\{+1,-1\}\) the operator system is formally equivalent to that of a composite spin

https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-52289-0_19/421179_1_En_19_IEq3_HTML.gif

system, the logical observables being isometries belonging to the Pauli group. Also in this approach fuzzy logic arises naturally when considering non-eigenvectors. The fuzzy membership function is obtained by the quantum mean value of the logical projector observable and turns out to be a probability measure in agreement with recent quantum cognition models. The analogy of many-valued logic with quantum angular momentum is then established. Logical observables for three-value logic are formulated as functions of the \(L_{z}\) observable of the orbital angular momentum \(\ell =1\). The representative 3-valued 2-argument logical observables for the \(\mathrm {Min}\) and \(\mathrm {Max}\) connectives are explicitly obtained.

François Dubois, Zeno Toffano

A New Perspective on Observables in the Category of Relations: A Spectral Presheaf for Relations

Abstract

We take a first step towards establishing a link between the topos approach to quantum theory and the monoidal approach to quantum theory. The topos approach to quantum theory makes extensive use of categories of commutative \(C^*\)-algebras and their corresponding Gelfand spectrum. We generalise these categories of \(C^*\)-algebras and generalise the notion of Gelfand spectrum via defining the abstract spectral presheaf. We then characterise this spectral presheaf for the category of sets and relations, and examine how this relates to the notion of observable in this category as studied in the monoidal approach to quantum theory.

Kevin Dunne

Language Geometry Using Random Indexing

Abstract

Random Indexing is a simple implementation of Random Projections with a wide range of applications. It can solve a variety of problems with good accuracy without introducing much complexity. Here we demonstrate its use for identifying the language of text samples, based on a novel method of encoding letter N-grams into high-dimensional Language Vectors. Further, we show that the method is easily implemented and requires little computational power and space. As proof of the method’s statistical validity, we show its success in a language-recognition task. On a difficult data set of 21,000 short sentences from 21 different languages, we achieve 97.4% accuracy, comparable to state-of-the-art methods.

Aditya Joshi, Johan T. Halseth, Pentti Kanerva

Backmatter

Titel: Quantum Interaction
herausgegeben von: Jose Acacio de Barros
Bob Coecke
Emmanuel Pothos
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-52289-0
Print ISBN: 978-3-319-52288-3
DOI: https://doi.org/10.1007/978-3-319-52289-0