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Andrei Khrennikov [29]Andrei Y. Khrennikov [1]Andrei Yu Khrennikov [1]
  1.  10
    The Present Situation in Quantum Theory and its Merging with General Relativity.Andrei Khrennikov - 2017 - Foundations of Physics 47 (8):1077-1099.
    We discuss the problems of quantum theory complicating its merging with general relativity. QT is treated as a general theory of micro-phenomena—a bunch of models. Quantum mechanics and quantum field theory are the most widely known. The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: (...)
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  2. The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics.Andrei Khrennikov - 2005 - Foundations of Physics 35 (10):1655-1693.
  3.  7
    A Macroscopic Violation of No-Signaling in Time Inequalities? How to Test Temporal Entanglement with Behavioral Observables.Patrizio E. Tressoldi, Markus A. Maier, Vanessa L. Buechner & Andrei Khrennikov - 2015 - Frontiers in Psychology 6.
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  4.  9
    On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements.Irina Basieva & Andrei Khrennikov - 2015 - Foundations of Physics 45 (10):1379-1393.
    In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility ) and separated reproducibility). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement (...)
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  5.  8
    Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 1.Andrei Khrennikov, Hans de Raedt, Arkady Plotnitsky & Sergey Polyakov - 2015 - Foundations of Physics 45 (7):707-710.
  6.  11
    Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 2.Andrei Khrennikov, Hans de Raedt, Arkady Plotnitsky & Sergey Polyakov - forthcoming - Foundations of Physics:1-4.
  7.  52
    Quantum-Like Model for Decision Making Process in Two Players Game.Masanari Asano, Masanori Ohya & Andrei Khrennikov - 2011 - Foundations of Physics 41 (3):538-548.
    In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained in (...)
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  8.  93
    CHSH Inequality: Quantum Probabilities as Classical Conditional Probabilities.Andrei Khrennikov - 2015 - Foundations of Physics 45 (7):711-725.
    In this note we demonstrate that the results of observations in the EPR–Bohm–Bell experiment can be described within the classical probabilistic framework. However, the “quantum probabilities” have to be interpreted as conditional probabilities, where conditioning is with respect to fixed experimental settings. Our approach is based on the complete account of randomness involved in the experiment. The crucial point is that randomness of selections of experimental settings has to be taken into account within one consistent framework covering all events related (...)
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  9. Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law.Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya & Ichiro Yamato - 2013 - Foundations of Physics 43 (7):895-911.
    There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological (...)
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  10.  23
    Preface of the Special Issue Quantum Foundations: Theory and Experiment. [REVIEW]Andrei Khrennikov & Gregor Weihs - 2012 - Foundations of Physics 42 (6):721-724.
  11.  17
    Preface.Ingemar Bengtsson & Andrei Khrennikov - 2011 - Foundations of Physics 41 (3):281-281.
  12.  81
    Frequency Analysis of the EPR-Bell Argumentation.Andrei Khrennikov - 2002 - Foundations of Physics 32 (7):1159-1174.
    We perform a frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-parameters need not contradict to the stabilization of (...)
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  13.  14
    Description of Composite Quantum Systems by Means of Classical Random Fields.Andrei Khrennikov - 2010 - Foundations of Physics 40 (8):1051-1064.
    Recently a new attempt to go beyond QM was performed in the form of so-called prequantum classical statistical field theory (PCSFT). In this approach quantum systems are described by classical random fields, e.g., the electron field or the neutron field. Averages of quantum observables arise as approximations of averages of classical variables (functionals of “prequantum fields”) with respect to fluctuations of fields. For classical variables given by quadratic functionals of fields, quantum and prequantum averages simply coincide. In this paper we (...)
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  14.  30
    Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology.Masanari Asano, Irina Basieva, Andrei Khrennikov, Masanori Ohya, Yoshiharu Tanaka & Ichiro Yamato - 2015 - Foundations of Physics 45 (10):1362-1378.
    We discuss foundational issues of quantum information biology —one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from “traditional quantum biophysics”. The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum mechanics (...)
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  15.  28
    Reality Without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics.Arkady Plotnitsky & Andrei Khrennikov - 2015 - Foundations of Physics 45 (10):1269-1300.
    First, this article considers the nature of quantum reality and the concept of realism in quantum theory, in conjunction with the roles of locality, causality, and probability and statistics there. Second, it offers two interpretations of quantum mechanics, developed by the authors of this article, the second of which is also a different theory of quantum phenomena. Both of these interpretations are statistical. The first interpretation, by A. Plotnitsky, “the statistical Copenhagen interpretation,” is nonrealist, insofar as the description or even (...)
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  16.  10
    Aims and Scope of the Special Issue, “Quantum Foundations: Informational Perspective”.Andrei Khrennikov & Blake C. Stacey - 2017 - Foundations of Physics 47 (8):1003-1008.
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  17.  34
    Complementarity of Mental Observables.Irina Basieva & Andrei Khrennikov - 2014 - Topics in Cognitive Science 6 (1):74-78.
    The aim of this note is to complete the discussion on the possibility of creation of quantum-like (QL) representation for the question order effect which was presented by Wang and Busemeyer (2013). We analyze the role of a fundamental feature of mental operators (given, e.g., by questions), namely, their complementarity.
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  18.  25
    Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process. [REVIEW]Andrei Khrennikov - 2011 - Foundations of Physics 41 (3):317-329.
    The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be (...)
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  19.  18
    Quantum Markov Model for Data From Shafir-Tversky Experiments in Cognitive Psychology.Luigi Accardi, Andrei Khrennikov & Masanori Ohya - 2009 - In Institute of Physics Krzysztof Stefanski (ed.), Open Systems and Information Dynamics. World Scientific Publishing Company. pp. 16--04.
  20.  13
    Reflections on Zeilinger–Brukner Information Interpretation of Quantum Mechanics.Andrei Khrennikov - 2016 - Foundations of Physics 46 (7):836-844.
    In this short review I present my personal reflections on Zeilinger–Brukner information interpretation of quantum mechanics.In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of irreducible quantum randomness is a very complicated issue which I plan to address in more detail. This note may be useful for general public interested in quantum foundations, especially because I try to analyze essentials of the information interpretation critically. This review is written in non-physicist friendly manner. Experts (...)
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  21.  23
    Detection Model Based on Representation of Quantum Particles by Classical Random Fields: Born's Rule and Beyond. [REVIEW]Andrei Khrennikov - 2009 - Foundations of Physics 39 (9):997-1022.
    Recently a new attempt to go beyond quantum mechanics (QM) was presented in the form of so called prequantum classical statistical field theory (PCSFT). Its main experimental prediction is violation of Born’s rule which provides only an approximative description of real probabilities. We expect that it will be possible to design numerous experiments demonstrating violation of Born’s rule. Moreover, recently the first experimental evidence of violation was found in the triple slit interference experiment, see Sinha, et al. (Foundations of Probability (...)
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  22.  21
    On Relations Between Probabilities Under Quantum and Classical Measurements.Andrei Y. Khrennikov & Elena R. Loubenets - 2004 - Foundations of Physics 34 (4):689-704.
    We show that the so-called quantum probabilistic rule, usually introduced in the physical literature as an argument of the essential distinction between the probability relations under quantum and classical measurements, is not, as it is commonly accepted, in contrast to the rule for the addition of probabilities of mutually exclusive events. The latter is valid under all experimental situations upon classical and quantum systems. We discuss also the quantum measurement situation that is similar to the classical one, described by the (...)
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  23.  7
    Towards Better Understanding QBism.Andrei Khrennikov - 2018 - Foundations of Science 23 (1):181-195.
    Recently I posted a paper entitled “External observer reflections on QBism”. As any external observer, I was not able to reflect all features of QBism properly. The comments I received from one of QBism’s creators, C. A. Fuchs, were very valuable to me in better understanding the views of QBists. Some of QBism’s features are very delicate and extracting them from articles of QBists is not a simple task. Therefore, I hope that the second portion of my reflections on QBism (...)
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  24.  15
    Photon Flux and Distance From the Source: Consequences for Quantum Communication.Andrei Khrennikov, Börje Nilsson, Sven Nordebo & Igor Volovich - 2014 - Foundations of Physics 44 (4):389-405.
    The paper explores the fundamental physical principles of quantum mechanics (in fact, quantum field theory) that limit the bit rate for long distances and examines the assumption used in this exploration that losses can be ignored. Propagation of photons in optical fibers is modelled using methods of quantum electrodynamics. We define the “photon duration” as the standard deviation of the photon arrival time; we find its asymptotics for long distances and then obtain the main result of the paper: the linear (...)
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  25.  9
    Unconditional Quantum Correlations Do Not Violate Bell’s Inequality.Andrei Khrennikov - 2015 - Foundations of Physics 45 (10):1179-1189.
    In this paper I demonstrate that the quantum correlations of polarization observables used in Bell’s argument against local realism have to be interpreted as conditional quantum correlations. By taking into account additional sources of randomness in Bell’s type experiments, i.e., supplementary to source randomness, I calculate the complete quantum correlations. The main message of the quantum theory of measurement is that complete correlations can be essentially smaller than the conditional ones. Additional sources of randomness diminish correlations. One can say another (...)
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  26.  25
    The Quantum-Like Brain on the Cognitive and Subcognitive Time Scales.Andrei Yu Khrennikov - 2008 - Journal of Consciousness Studies 15 (7):39-77.
    This article takes as its point of departure the view that the discovery of the mathematical formalism of quantum mechanics (QM) was not merely a discovery of a new mathematical way of dealing with physical, and specifically quantum, processes in nature. It was also a discovery of a general mathematical formalism (in part discovered in mathematics itself earlier), which, supplemented by certain additional rules, consistently described the processing of incomplete information about certain events and contexts in which these events occur. (...)
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  27.  4
    Quantum-Like Model of Unconscious–Conscious Dynamics.Andrei Khrennikov - 2015 - Frontiers in Psychology 6.
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  28.  5
    Towards a Field Model of Prequantum Reality.Andrei Khrennikov - 2012 - Foundations of Physics 42 (6):725-741.
    We start with an extended review of classical field approaches to quantum mechanics (QM). In particular, we present Einstein’s dream to exclude particles totally from quantum physics. We also describe the evolution of Einstein’s views: from the invention of the light quantum to a purely classical field picture of quantum reality. Then we present briefly a new field-type model, prequantum classical statistical field theory (PCSFT), which was recently developed in a series of the author’s papers. PCSFT reproduces basic predictions of (...)
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