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Baladron, C. & Khrennikov, A. (2019). Bell inequality violation in the framework of a Darwinian approach to quantum mechanics. The European Physical Journal Special Topics, 227(15-16), 2119-2132
Open this publication in new window or tab >>Bell inequality violation in the framework of a Darwinian approach to quantum mechanics
2019 (English)In: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 227, no 15-16, p. 2119-2132Article, review/survey (Refereed) Published
Abstract [en]

A fundamental particle in physical space subject to conservation of momentum and energy, and characterized by its average mass and its position is methodologically supplemented with an information processor - a classical Turing machine - and a randomizer both defined on an information space localized on every particle. In this way the particle can be considered a generalized Darwinian system on which natural selection could act steering the evolution on the information space of the algorithms that govern the behaviour of the particles, giving rise plausibly to emergent quantum behaviour from initial randomness. This theory is applied to an EPR-Bohm experiment for electrons in order to analyse Bell inequality violation. A model for the entanglement of two particles has been considered. The model includes shared randomness - each particle stores its own randomizer and that of its partner - and the mutual transfer of their algorithms - sharing programs - that contain their respective anticipation modules. This fact enables every particle to anticipate not only the possible future configurations of its surrounding systems, but also those of the surrounding systems of its entangled partner. Thus, while preserving locality and realism, this theory implies outcome dependence - through shared randomness - and parameter dependence - through shared anticipation - for entangled states and, as a consequence, the violation of the Bell inequality in an EPR-Bohm experiment.

Place, publisher, year, edition, pages
Springer, 2019
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-81846 (URN)10.1140/epjst/e2019-800061-1 (DOI)000462523100023 ()2-s2.0-85062772552 (Scopus ID)
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-08-29Bibliographically approved
Khrennikov, A. & Alodjants, A. (2019). Classical (Local and Contextual) Probability Model for Bohm-Bell Type Experiments: No-Signaling as Independence of Random Variables. Entropy, 21(2), 1-20, Article ID 157.
Open this publication in new window or tab >>Classical (Local and Contextual) Probability Model for Bohm-Bell Type Experiments: No-Signaling as Independence of Random Variables
2019 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 2, p. 1-20, article id 157Article, review/survey (Refereed) Published
Abstract [en]

We start with a review on classical probability representations of quantum states and observables. We show that the correlations of the observables involved in the Bohm-Bell type experiments can be expressed as correlations of classical random variables. The main part of the paper is devoted to the conditional probability model with conditioning on the selection of the pairs of experimental settings. From the viewpoint of quantum foundations, this is a local contextual hidden-variables model. Following the recent works of Dzhafarov and collaborators, we apply our conditional probability approach to characterize (no-)signaling. Consideration of the Bohm-Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science. The main message of this paper (rooted to Ballentine) is that quantum probabilities and more generally probabilities related to the Bohm-Bell type experiments (not only in physics, but also in psychology, sociology, game theory, economics, and finances) can be classically represented as conditional probabilities.

Place, publisher, year, edition, pages
MDPI, 2019
Keywords
quantum versus classical probability, Bohm-Bell type experiments in physics and psychology, localty, contextual hidden-variables models, (no-)signaling, random generators, selection of experimental settings, conditional probability
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-81409 (URN)10.3390/e21020157 (DOI)000460742200058 ()2-s2.0-85061988569 (Scopus ID)
Available from: 2019-03-29 Created: 2019-03-29 Last updated: 2019-08-29Bibliographically approved
Khrennikov, A. (2019). Classical versus quantum probability: Comments on the paper "On universality of classical probability with contextually labeled random variables" by E. Dzhafarov and M. Kon. Journal of mathematical psychology (Print), 89, 87-92
Open this publication in new window or tab >>Classical versus quantum probability: Comments on the paper "On universality of classical probability with contextually labeled random variables" by E. Dzhafarov and M. Kon
2019 (English)In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 89, p. 87-92Article in journal, Editorial material (Other academic) Published
Abstract [en]

Recently Dzhafarov and Kon published the paper advertising the possibility to use the coupling technique of classical probability theory to model incompatible observables in quantum physics and quantum-like models of psychology. Here I present comments on this paper by stressing advantages and disadvantages. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Classical and quantum probability calculi, Incompatible observables, Joint probability distribution, Coupling, Bell-Dzhafarov-Kujala inequality, No-signaling, Contextuality
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-81838 (URN)10.1016/j.jmp.2018.10.005 (DOI)000462805300006 ()
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically approved
Khrennikov, A., Toffano, Z. & Dubois, F. (2019). Concept of information laser: from quantum theory to behavioural dynamics. The European Physical Journal Special Topics, 227(15-16), 2133-2153
Open this publication in new window or tab >>Concept of information laser: from quantum theory to behavioural dynamics
2019 (English)In: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 227, no 15-16, p. 2133-2153Article, review/survey (Refereed) Published
Abstract [en]

Recently, the methods of quantum theory, especially quantum information, started to be widely applied outside of physics: in cognitive, social sciences, economics, finance, decision making and biology. We propose a quantum-like model: the information laser. The basic assumption is the discrete structure of state spaces related to the quantization of information. The information field acts in the form of indistinguishable quanta of social energy analogue to photons. The massive flow of information acts as a laser pump. In this framework, an information selection process by agents under constant pressure of massive repeated information leads to collective resonance effects in analogy with laser cavity and stimulated emission. In order to make operational parallels between physical lasers and the information laser we identify the essential features of laser operation. An application to the analysis of recent disruptive social events (colour revolutions) is discussed. Social analogues to the laser are also considered through the model of Echo Chambers induced by the Internet and Adam Smith's invisible hand.

Place, publisher, year, edition, pages
Springer, 2019
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-81847 (URN)10.1140/epjst/e2018-800027-6 (DOI)000462523100024 ()2-s2.0-85062700446 (Scopus ID)
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-08-29Bibliographically approved
Yurova, E. & Khrennikov, A. (2019). Description of (Fully) Homomorphic Cryptographic Primitives Within the p-Adic Model of Encryption. In: Karl‐Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Wahlberg (Ed.), Analysis, Probability, Applications, and Computation: Proceedings of the 11th ISAAC Congress, Växjö (Sweden) 2017. Paper presented at 11th ISAAC Congress, Växjö, Sweden, 2017 (pp. 241-248). Cham: Birkhäuser Verlag
Open this publication in new window or tab >>Description of (Fully) Homomorphic Cryptographic Primitives Within the p-Adic Model of Encryption
2019 (English)In: Analysis, Probability, Applications, and Computation: Proceedings of the 11th ISAAC Congress, Växjö (Sweden) 2017 / [ed] Karl‐Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Wahlberg, Cham: Birkhäuser Verlag, 2019, p. 241-248Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider a description of homomorphic and fully homomorphic cryptographic primitives in the p-adic model. This model describes a wide class of ciphers (including substitution ciphers, substitution ciphers streaming, keystream ciphers in the alphabet of p elements), but certainly not all. Homomorphic and fully homomorphic ciphers are used to ensure the credibility of remote computing, including cloud technology. Within considered p-adic model we describe all homomorphic cryptographic primitives with respect to arithmetic and coordinate-wise logical operations in the ring of p-adic integers ℤ p . We show that there are no fully homomorphic cryptographic primitives for each pair of the considered set of arithmetic and coordinate-wise logical operations on ℤ p.

Place, publisher, year, edition, pages
Cham: Birkhäuser Verlag, 2019
Series
Trends in Mathematics, ISSN 2297-0215, E-ISSN 2297-024X
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
urn:nbn:se:lnu:diva-82771 (URN)10.1007/978-3-030-04459-6_23 (DOI)2-s2.0-85065438988 (Scopus ID)978-3-030-04458-9 (ISBN)978-3-030-04459-6 (ISBN)
Conference
11th ISAAC Congress, Växjö, Sweden, 2017
Available from: 2019-05-27 Created: 2019-05-27 Last updated: 2019-08-29Bibliographically approved
Rashkovskiy, S. & Khrennikov, A. (2019). Generalized Fock space and contextuality. Philosophical Transactions. Series A: Mathematical, physical, and engineering science, 377(2157), Article ID 20190096.
Open this publication in new window or tab >>Generalized Fock space and contextuality
2019 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 377, no 2157, article id 20190096Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to linear space representations of contextual probabilities-in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way, we reproduce the Doi-Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability-by the magnitude of the interference term. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

Place, publisher, year, edition, pages
Royal Society, 2019
Keywords
Fock space, Doi-Peliti formalism, quantum probability, contextuality, interference of probabilities, calculi of creation-annihilation operators
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-89408 (URN)10.1098/rsta.2019.0096 (DOI)000486318400007 ()31522648 (PubMedID)
Available from: 2019-10-03 Created: 2019-10-03 Last updated: 2019-10-03Bibliographically approved
Khrennikov, A. (2019). Get Rid of Nonlocality from Quantum Physics. Entropy, 21(8), 1-15, Article ID 806.
Open this publication in new window or tab >>Get Rid of Nonlocality from Quantum Physics
2019 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 21, no 8, p. 1-15, article id 806Article in journal (Refereed) Published
Abstract [en]

This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of the Bohr complementarity principle. Thus, the attempts to couple experimental violations of the Bell type inequalities with "quantum nonlocality" is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single electron or the polarization projections for a single photon. Of course, one can go beyond quantum theory with the hidden variables models (as was suggested by Bell) and then discuss their possible nonlocal features. However, conventional quantum theory is local.

Place, publisher, year, edition, pages
MDPI, 2019
Keywords
Bell type inequality, nonlocality, action at a distance, incompatibility, Landau identity, complementarity principle, Bell operator, squared Bell operator, Hertz-Boltzmann Bild methodology, prequantum classical statistical field theory
National Category
Mathematics Physical Sciences
Research subject
Natural Science, Physics; Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-89285 (URN)10.3390/e21080806 (DOI)000483732700045 ()
Available from: 2019-09-25 Created: 2019-09-25 Last updated: 2019-09-25Bibliographically approved
Wu, B. & Khrennikov, A. (2019). p-Adic Analogue of the Wave Equation. Journal of Fourier Analysis and Applications, 25(5), 2447-2462
Open this publication in new window or tab >>p-Adic Analogue of the Wave Equation
2019 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 25, no 5, p. 2447-2462Article in journal (Refereed) Published
Abstract [en]

In this paper, a p-adic analogue of the wave equation with Lipschitz source is considered. Since it is hard to arrive the solution of the problem, we propose a regularized method to solve the problem from a modified p-adic integral equation. Moreover, we give an iterative scheme for numerical computation of the regularlized solution.

Place, publisher, year, edition, pages
Springer, 2019
Keywords
Cauchy problem, p-Adic elliptic equation, Regularized solution
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-90853 (URN)10.1007/s00041-019-09668-y (DOI)000504219600006 ()
Available from: 2020-01-10 Created: 2020-01-10 Last updated: 2020-01-10Bibliographically approved
Pothos, E. M., Basieva, I., Khrennikov, A. & Yearsley, J. M. (2019). Perspectives on Correctness in Probabilistic Inference from Psychology. The Spanish Journal of Psychology, 22, 1-12, Article ID E55.
Open this publication in new window or tab >>Perspectives on Correctness in Probabilistic Inference from Psychology
2019 (English)In: The Spanish Journal of Psychology, ISSN 1138-7416, E-ISSN 1988-2904, Vol. 22, p. 1-12, article id E55Article in journal (Refereed) Published
Abstract [en]

Research into decision making has enabled us to appreciate that the notion of correctness is multifaceted. Different normative framework for correctness can lead to different insights about correct behavior. We illustrate the shifts for correctness insights with two tasks, the Wason selection task and the conjunction fallacy task; these tasks have had key roles in the development of logical reasoning and decision making research respectively. The Wason selection task arguably has played an important part in the transition from understanding correctness using classical logic to classical probability theory (and information theory). The conjunction fallacy has enabled a similar shift from baseline classical probability theory to quantum probability. The focus of this overview is the latter, as it represents a novel way for understanding probabilistic inference in psychology. We conclude with some of the current challenges concerning the application of quantum probability theory in psychology in general and specifically for the problem of understanding correctness in decision making.

Place, publisher, year, edition, pages
Cambridge University Press, 2019
Keywords
conjunction fallacy, decision making, quantum theory
National Category
Mathematics Psychology
Research subject
Mathematics, Applied Mathematics; Social Sciences, Psychology
Identifiers
urn:nbn:se:lnu:diva-90854 (URN)10.1017/sjp.2019.48 (DOI)000503979400001 ()31868162 (PubMedID)
Available from: 2020-01-10 Created: 2020-01-10 Last updated: 2020-01-10Bibliographically approved
Tsarev, D., Trofimova, A., Alodjants, A. & Khrennikov, A. (2019). Phase transitions, collective emotions and decision-making problem in heterogeneous social systems. Scientific Reports, 9, 1-13, Article ID 18039.
Open this publication in new window or tab >>Phase transitions, collective emotions and decision-making problem in heterogeneous social systems
2019 (English)In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 9, p. 1-13, article id 18039Article in journal (Refereed) Published
Abstract [en]

The paper considers the problem of collective decision-making as a second order phase-transition, which occurs in heterogeneous information-oriented communities possessing frequent information exchange between individuals. We examine the quantum-like model of simplified two-level cognitive systems (TLCS) interacting with a socially important (contextual) information field. The model exploits approaches to the modern social cohesion framework. We refer to some target network community, which is in close interaction (e.g. message exchange) with "reservour" (large network community) possessing infinite degree of freedom. We introduce a new approach for valence and arousal variables, used in cognitive sciences for the description of collective emotion states. We express them via collective polarization and population imbalance respectively. The model predicts a super-radiant phase transition for target network community leading to coherent polarization establishment in the socium. The valence and arousal parameters can be evaluated from actrors behaviour in social network communities as a result of immediate response (decision-making) to some notable news. We introduce Gaussian and Levy distribution functions to reveal the influence of social community inhomogeneity on decision-making features. We show that a critical (social) temperature is determined by the population imbalance (valence), detuning, field coupling strength parameter and relay to conditions of social polarization establishment. We predict coherent social energy release in a community without inversion due to its specific properties close to the superfluid paradigm in quantum physics, or social cohesion in sociology. We establish a connection of our model to the recently presented quantum-like model of the social laser to describe the waves of social protests as the result of collective decision-making process in the system with inversion of population in mental states. Finally, we compare our model with existing social impact models, a.k.a. cellular automata models, in the limit when social community perceives information field in the state induced by large information reservoir (mass-media). Notably, eliminating quantized field we lose important information how collective emotions (arousal) form in social community.

Place, publisher, year, edition, pages
Nature Publishing Group, 2019
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-90620 (URN)10.1038/s41598-019-54296-7 (DOI)000500553200001 ()31792361 (PubMedID)
Available from: 2019-12-19 Created: 2019-12-19 Last updated: 2019-12-19Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

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