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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 ()
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically 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 ()
Available from: 2019-03-29 Created: 2019-03-29 Last updated: 2019-03-29Bibliographically 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 ()
Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically approved
Antoniouk, A. V., Oleschko, K., Kochubei, A. N. & Khrennikov, A. (2018). A stochastic p-adic model of the capillary flow in porous random medium. Physica A: Statistical Mechanics and its Applications, 505, 763-777
Open this publication in new window or tab >>A stochastic p-adic model of the capillary flow in porous random medium
2018 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 505, p. 763-777Article in journal (Refereed) Published
Abstract [en]

We develop the p-adic model of propagation of fluids (e.g., oil or water) in capillary networks in a porous random medium. The hierarchic structure of a system of capillaries is mathematically modeled by endowing trees of capillaries with the structure of an ultra metric space. Considerations are restricted to the case of idealized networks represented by homogeneous p-trees with p branches leaving each vertex, where p > 1 is a prime number. Such trees are realized as the fields of p-adic numbers. We introduce and study an inhomogeneous Markov process describing the penetration of fluid into a porous random medium. (C) 2018 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
P-adic numbers, P-adic theoretical physics, Porous random medium, Capillary network, Penetration of fluid, Inhomogeneous Markov process
National Category
Physical Sciences Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76948 (URN)10.1016/j.physa.2018.03.049 (DOI)000437061000067 ()
Available from: 2018-07-19 Created: 2018-07-19 Last updated: 2019-02-22Bibliographically approved
Baladron, C. & Khrennikov, A. (2018). At the Crossroads of Three Seemingly Divergent Approaches to Quantum Mechanics. In: A. Khrennikov, B. Toni (Ed.), Quantum Foundations, Probability and Information: (pp. 13-21). Springer
Open this publication in new window or tab >>At the Crossroads of Three Seemingly Divergent Approaches to Quantum Mechanics
2018 (English)In: Quantum Foundations, Probability and Information / [ed] A. Khrennikov, B. Toni, Springer, 2018, p. 13-21Chapter in book (Refereed)
Abstract [en]

Several concepts stemming from three apparently divergent approaches to quantum mechanics—Bohmian Mechanics, QBism, and Time-Symmetric Quantum Mechanics—are interwoven in an information-theoretic Darwinian scheme applied to fundamental physical systems that might contribute to shed light on some long-standing quantum mechanical conundrums.

Place, publisher, year, edition, pages
Springer, 2018
Series
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, ISSN 2520-193X
Keywords
Quantum mechanical foundations; Darwinian evolution; Adaptive dynamics; Quantum information; Information theory
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79083 (URN)10.1007/978-3-319-74971-6_2 (DOI)978-3-319-74970-9 (ISBN)978-3-319-74971-6 (ISBN)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-11Bibliographically approved
Khrennikov, A. & Loubenets, E. R. (2018). Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations. Entropy, 20(11), Article ID 829.
Open this publication in new window or tab >>Evaluating the Maximal Violation of the Original Bell Inequality by Two-Qudit States Exhibiting Perfect Correlations/Anticorrelations
2018 (English)In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 20, no 11, article id 829Article in journal (Refereed) Published
Abstract [en]

We introduce the general class of symmetric two-qubit states guaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomes whenever some spin observable is measured at both sites. We prove that, for all states from this class, the maximal violation of the original Bell inequality is upper bounded by 32" role="presentation">32 and specify the two-qubit states where this quantum upper bound is attained. The case of two-qutrit states is more complicated. Here, for all two-qutrit states, we obtain the same upper bound 32" role="presentation">32 for violation of the original Bell inequality under Alice and Bob spin measurements, but we have not yet been able to show that this quantum upper bound is the least one. We discuss experimental consequences of our mathematical study.

Place, publisher, year, edition, pages
MDPI, 2018
Keywords
original Bell inequality; perfect correlation/anticorrelation; qudit states; quantum bound; measure of classicality
National Category
Computational Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79077 (URN)10.3390/e20110829 (DOI)000451308800021 ()
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-13Bibliographically approved
Khrennikov, A. (2018). External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications. In: A. Khrennikov, B. Toni (Ed.), Quantum Foundations, Probability and Information: (pp. 93-118). Springer
Open this publication in new window or tab >>External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications
2018 (English)In: Quantum Foundations, Probability and Information / [ed] A. Khrennikov, B. Toni, Springer, 2018, p. 93-118Chapter in book (Refereed)
Abstract [en]

In this critical essay, I present my personal reflections on QBism. I have no intrinsic sympathy neither to QBism nor to subjective interpretation of probability in general. However, I have been following the development of QBism from its very beginning, observing its evolution and success, sometimes with big surprise. Therefore my reflections on QBism can be treated as “external observer” reflections. I hope that my view on this interpretation of quantum mechanics (QM) has some degree of objectivity. It may be useful for researchers who are interested in quantum foundations, but do not belong to the QBism community, because I tried to analyze essentials of QBism critically (i.e., not just emphasizing its advantages, as in a typical QBist publication). QBists, too, may be interested in comments of an external observer who monitored development of this approach to QM during the last 16 years. (However, this paper cannot serve as an introduction to QBism. It neither concerns the philosophic issues around QBism.) Two sections are devoted to comparison of QBism with two interpretations of QM, the Växjö and information interpretations, which are close to QBism in two very different aspects, probabilistic and informational. The second part of the paper is devoted to interpretations of probability, objective versus subjective, and views of Kolmogorov, von Mises, and de Finetti. De Finetti’s approach to methodology of science is presented and compared with QBism. One of the outputs of this comparison is understanding of restrictiveness of QBism, where the subjective probability viewpoint is applied only to QM. One of the main messages of this paper is that QBism has to be completed by CBism (classical physics Bayesianism). Finally, the possibility to use QBism as the general interpretational basis for applications of the quantum probabilistic formalism for decision-making outside of physics (in cognitive, social, and political sciences, psychology, economics, finances) is considered.

Place, publisher, year, edition, pages
Springer, 2018
Series
STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, ISSN 2520-193X, E-ISSN 2520-1948
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-79082 (URN)10.1007/978-3-319-74971-6_9 (DOI)978-3-319-74970-9 (ISBN)978-3-319-74971-6 (ISBN)
Available from: 2018-12-05 Created: 2018-12-05 Last updated: 2018-12-10Bibliographically approved
Lozada Aguilar, M. A., Khrennikov, A. & Oleschko, K. (2018). From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems. Philosophical Transactions. Series A: Mathematical, physical, and engineering science, 376(2118), Article ID 20170225.
Open this publication in new window or tab >>From axiomatics of quantum probability to modelling geological uncertainty and management of intelligent hydrocarbon reservoirs with the theory of open quantum systems
2018 (English)In: Philosophical Transactions. Series A: Mathematical, physical, and engineering science, ISSN 1364-503X, E-ISSN 1471-2962, Vol. 376, no 2118, article id 20170225Article in journal (Refereed) Published
Abstract [en]

As was recently shown by the authors, quantum probability theory can be used for the modelling of the process of decision-making (e.g. probabilistic risk analysis) for macroscopic geophysical structures such as hydrocarbon reservoirs. This approach can be considered as a geophysical realization of Hilbert's programme on axiomatization of statistical models in physics (the famous sixth Hilbert problem). In this conceptual paper, we continue development of this approach to decision-making under uncertainty which is generated by complexity, variability, heterogeneity, anisotropy, as well as the restrictions to accessibility of subsurface structures. The belief state of a geological expert about the potential of exploring a hydrocarbon reservoir is continuously updated by outputs of measurements, and selection of mathematical models and scales of numerical simulation. These outputs can be treated as signals Dfrom the information environment E. The dynamics of the belief state can be modelled with the aid of the theory of open quantum systems: a quantum state (representing uncertainty in beliefs) is dynamically modified through coupling with E; stabilization to a steady state determines a decision strategy. In this paper, the process of decision-making about hydrocarbon reservoirs (e.g. 'explore or not?'; 'open new well or not?'; 'contaminated by water or not?'; 'double or triple porosity medium?') is modelled by using the Gorini-Kossakowski- Sudarshan-Lindblad equation. In our model, this equation describes the evolution of experts' predictions about a geophysical structure. We proceed with the information approach to quantum theory and the subjective interpretation of quantum probabilities (due to quantum Bayesianism).

Keywords
decision-making and risk analysis, geology, Hilbert's sixth problem, quantum versus classical Bayesian inference, heterogeneity, open quantum systems
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-76464 (URN)10.1098/rsta.2017.0225 (DOI)000427878700004 ()29555799 (PubMedID)
Available from: 2018-07-10 Created: 2018-07-10 Last updated: 2019-02-22Bibliographically approved
Haven, E., Khrennikov, A., Ma, C. & Sozzo, S. (2018). Introduction to quantum probability theory and its economic applications. Journal of Mathematical Economics, 78, 127-130
Open this publication in new window or tab >>Introduction to quantum probability theory and its economic applications
2018 (English)In: Journal of Mathematical Economics, ISSN 0304-4068, E-ISSN 1873-1538, Vol. 78, p. 127-130Article in journal, Editorial material (Other academic) Published
Place, publisher, year, edition, pages
Elsevier, 2018
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-78740 (URN)10.1016/j.jmateco.2018.08.004 (DOI)000448495000015 ()
Available from: 2018-11-08 Created: 2018-11-08 Last updated: 2018-11-08Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9857-0938

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