•  30
    Logical Approach to p-adic Probabilities
    Bulletin of the Section of Logic 35 (1): 49-57. 2006.
  •  48
    The quantum-like brain on the cognitive and subcognitive time scales
    Journal of Consciousness Studies 15 (7): 39-77. 2008.
    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…Read more
  •  14
    The Ozawa’s intersubjectivity theorem (OIT) proved within quantum measurement theory supports the new postulate of relational quantum mechanics (RQM), the postulate on internally consistent descriptions. But from OIT viewpoint postulate’s formulation should be completed by the assumption of probability reproducibility. We remark that this postulate was proposed only recently to resolve the problem of intersubjectivity of information in RQM. In contrast to RQM for which OIT is a supporting theore…Read more
  •  16
    Quantum-like structure is present practically everywhere. Quantum-like models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application o…Read more
  •  50
    Decision Theory and Choices: A Complexity Approach (edited book)
    with Marisa Faggini, Concetto Paolo Vinci, Antonio Abatemarco, Rossella Aiello, F. T. Arecchi, Lucio Biggiero, Giovanna Bimonte, Sergio Bruno, Carl Chiarella, Maria Pia Di Gregorio, Giacomo Di Tollo, Simone Giansante, Jaime Gil Aluja, Marianna Lyra, Riccardo Meucci, Guglielmo Monaco, Giancarlo Nota, Serena Sordi, Pietro Terna, Kumaraswamy Velupillai, and Alessandro Vercelli
    Springer Verlag Italia. 2010.
    The New Economic Windows Series, derived from Massimo Salzano's ideas and work, incorporates material from textbooks, monographs and conference proceedings that deals with both the theoretical and applied aspects of various sub-disciplines ...
  •  9
    As previous Växjö conferences on quantum foundations, QTRF-5 was notable not only for the contributions of the papers presented there but also for its exciting debates. These debates offered a great diversity of opinions on foundations of quantum mechanics (QM) and its future developments: from those defined by the view of those who adhere to the orthodox Copenhagen interpretation (which rejected realism and causality), at one end of the spectrum, to those who subscribed to realist views of the …Read more
  • Quantum theory: reconsideration of foundations-3: Växjö, Sweden, 6-11 June 2005 (edited book)
    with Guillaume Adenier and Theo M. Nieuwenhuizen
    American Institute of Physics. 2006.
    This Växjö conference was devoted to the reconsideration of quantum foundations. Due to increasing research in quantum information theory, especially on quantum computing and cryptography, many questions regarding the foundations of quantum mechanics, which have long been considered to be exclusively of philosophical interest, nowadays play an important role in theoretical and experimental quantum physics.
  •  56
    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…Read more
  •  49
    What are the appropriate axioms of rationality for reasoning under uncertainty with resource-constrained systems?
    with Harald Atmanspacher, Irina Basieva, Jerome R. Busemeyer, Emmanuel M. Pothos, Richard M. Shiffrin, and Zheng Wang
    Behavioral and Brain Sciences 43. 2020.
    When constrained by limited resources, how do we choose axioms of rationality? The target article relies on Bayesian reasoning that encounter serioustractabilityproblems. We propose another axiomatic foundation: quantum probability theory, which provides for less complex and more comprehensive descriptions. More generally, defining rationality in terms of axiomatic systems misses a key issue: rationality must be defined by humans facing vague information.
  •  41
    Unconditional Quantum Correlations do not Violate Bell’s Inequality
    Foundations of Physics 45 (10): 1179-1189. 2015.
    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 one…Read more
  •  77
    Reality Without Realism: On the Ontological and Epistemological Architecture of Quantum Mechanics
    with Arkady Plotnitsky
    Foundations of Physics 45 (10): 1269-1300. 2015.
    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 interpretati…Read more
  •  43
    A macroscopic violation of no-signaling in time inequalities? How to test temporal entanglement with behavioral observables
    with Patrizio E. Tressoldi, Markus A. Maier, and Vanessa L. Buechner
    Frontiers in Psychology 6. 2015.
  •  21
    The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus
    with Irina Basieva, Eric Guerci, Sébastien Duchêne, and Ismaël Rafaï
    Theory and Decision 92 (2): 387-406. 2021.
    Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment—the basic quantum interference experiment. In this paper, we report on an economics experiment based on a triple-slit experiment design, where the slits are menus of alternatives from which one can choose. Th…Read more
  •  49
    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”) class…Read more
  •  64
    Formal Foundations for the Origins of Human Consciousness
    with Giuseppe Iurato and Fionn Murtagh
    P-Adic Numbers, Ultrametric Analysis, and Applications 8 (4): 249-279. 2016.
    In the framework of p-adic analysis (the simplest version of analysis on trees in which hierarchic structures are presented through ultrametric distance) applied to formalize psychic phenomena, we would like to propose some possible first hypotheses about the origins of human consciousness centered on the basic notion of time symmetry breaking as meant according to quantum field theory of infinite systems. Starting with Freud's psychophysical (hydraulic) model of unconscious and conscious flows …Read more
  •  33
    Quantum Markov model for data from Shafir-Tversky experiments in cognitive psychology
    with Luigi Accardi and Masanori Ohya
    In Krzysztof Stefanski (ed.), Open Systems and Information Dynamics, World Scientific Publishing Company. pp. 16--04. 2009.
  •  25
    Towards a Field Model of Prequantum Reality
    Foundations of Physics 42 (6): 725-741. 2012.
    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. …Read more
  •  23
    Preface of the Special Issue Probing the Limits of Quantum Mechanics: Theory and Experiment, Volume 1
    with Hans de Raedt, Arkady Plotnitsky, and Sergey Polyakov
    Foundations of Physics 45 (7): 707-710. 2015.
  •  159
    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 ac…Read more
  •  28
    The year 2019 witnessed the 20th Jubileum of the Växjö conference series on quantum foundations and probability in physics. This has been the longest running series of conferences on the subject in history. Many old and new friendships were forged at Linnaeus University and the beautiful surrounding lakes of Småland, where once yearly everyone gathers to renew the debate and report their latest progress. 2019 also represents the Porcelain Anniversary—18 years—of the point of view on quantum theo…Read more
  •  169
    We presented a contextual statistical model of the probabilistic description of physical reality. Here contexts (complexes of physical conditions) are considered as basic elements of reality. There is discussed the relation with QM. We propose a realistic analogue of Bohr’s principle of complementarity. In the opposite to the Bohr’s principle, our principle has no direct relation with mutual exclusivity for observables. To distinguish our principle from the Bohr’s principle and to give better ch…Read more
  •  159
    Non-Kolmogorovian Approach to the Context-Dependent Systems Breaking the Classical Probability Law
    with Masanari Asano, Irina Basieva, Masanori Ohya, and Ichiro Yamato
    Foundations of Physics 43 (7): 895-911. 2013.
    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…Read more
  •  29
    We present a quantum mechanical analysis of Bell’s approach to quantum foundations based on his hidden-variable model. We claim and try to justify that the Bell model contradicts to the Heinsenberg’s uncertainty and Bohr’s complementarity principles. The aim of this note is to point to the physical seed of the aforementioned principles. This is the Bohr’s quantum postulate: the existence of indivisible quantum of action given by the Planck constant h. By contradicting these basic principles of Q…Read more
  •  111
    Frequency Analysis of the EPR-Bell Argumentation
    Foundations of Physics 32 (7): 1159-1174. 2002.
    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-para…Read more
  •  88
    Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology
    with Masanari Asano, Irina Basieva, Masanori Ohya, Yoshiharu Tanaka, and Ichiro Yamato
    Foundations of Physics 45 (10): 1362-1378. 2015.
    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-system…Read more
  •  15
    Thermodynamic-like approach to complexity of the financial market (in the light of the present financial crises)
    In Marisa Faggini, Concetto Paolo Vinci, Antonio Abatemarco, Rossella Aiello, F. T. Arecchi, Lucio Biggiero, Giovanna Bimonte, Sergio Bruno, Carl Chiarella, Maria Pia Di Gregorio, Giacomo Di Tollo, Simone Giansante, Jaime Gil Aluja, A. I͡U Khrennikov, Marianna Lyra, Riccardo Meucci, Guglielmo Monaco, Giancarlo Nota, Serena Sordi, Pietro Terna, Kumaraswamy Velupillai & Alessandro Vercelli (eds.), Decision Theory and Choices: A Complexity Approach, Springer Verlag Italia. pp. 183--203. 2010.