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  • 1.
    Adenier, Guillaume
    et al.
    Oslo University.
    Ohya, Masanori
    Tokyo University of Science.
    Watanabe, Noboru
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Double Blinding-Attack on Entanglement-Based Quantum Key Distribution Protocols2012In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1424, no 1, p. 9-16Article in journal (Refereed)
    Abstract [en]

    We propose a double blinding-attack on entangled-based quantum key distribution protocols. The principle of the attack is the same as in existing blinding attack except that instead of blinding the detectors on one side only, Eve is blinding the detectors of both Alice and Bob. In the BBM92 protocol, the attack allows Eve to get a full knowledge of the key and remain undetected even if Alice and Bob are using 100% efficient detectors. The attack can be easily extended to Ekert protocol, with an efficiency as high as 85.3%.

  • 2.
    Adenier, Guillaume
    et al.
    University of Oslo, Norway.
    Watanabe, Noboru
    Tokyo University of Science, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Multiple-photon absorption attack on entanglement-based quantum key distribution protocols2013In: Quantum Bio-Informatics V: Proceedings of the Quantum Bio-Informatics 2011 : Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, Singapore: World Scientific, 2013, vol. 30, p. 171-180Conference paper (Refereed)
    Abstract [en]

    We propose a multiple-photon absorption attack on Quantum Key Distribution protocols. In this attack, the eavesdropper (Eve) is in control of the source and sends pulses correlated in polarization (but not entangled) containing several photons at frequencies for which only multiple-photon absorptions are possible in Alice's and Bob's detectors. Whenever the number of photons from one pulse are dispatched in insufficient number to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature is enough to reproduce the type of statistics on the detected pulses that are considered as indicating a secure quantum key distribution in entangled-based protocols, even though the source is controlled by Eve, and we discuss possible countermeasures.

  • 3.
    Asano, M
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, M
    Tokyo University of Science.
    Tanaka, Y
    Tokyo University of Science.
    Quantum-Like Representation of Non-Bayesian Inference2013In: Quantum Bio-Informatics V - Proceedings of the Quantum Bio-Informatics 2011: Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, World Scientific, 2013, p. 57-67Conference paper (Refereed)
    Abstract [en]

    This research is related to the problem of “irrational decision making or inference” that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe “psychological factor” disturbing “rationality” as an “environment” correlating with the “main system” of usual Bayesian inference.

  • 4.
    Asano, M
    et al.
    Tokyo University of Science.
    Ohya, M
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    General Formalism of Decision Making Based on Theory of Open Quantum Systems2013In: Quantum Bio-Informatics V - Proceedings of the Quantum Bio-Informatics 2011: Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, and Masanori Ohya, World Scientific, 2013, p. 49-56Conference paper (Refereed)
    Abstract [en]

    We present the general formalism of decision making which is based on the theory of open quantum systems. A person (decision maker), say Alice, is considered as a quantum-like system, i.e., a system which information processing follows the laws of quantum information theory. To make decision, Alice interacts with a huge mental bath. Depending on context of decision making this bath can include her social environment, mass media (TV, newspapers, INTERNET), and memory. Dynamics of an ensemble of such Alices is described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. We speculate that in the processes of evolution biosystems (especially human beings) designed such “mental Hamiltonians” and GKSL-operators that any solution of the corresponding GKSL-equation stabilizes to a diagonal density operator (In the basis of decision making.) This limiting density operator describes population in which all superpositions of possible decisions has already been resolved. In principle, this approach can be used for the prediction of the distribution of possible decisions in human populations.

  • 5. Asano, M
    et al.
    Ohya, M
    Tanaka, Y
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum uncertainty and decision-making in game theory2011In: Quantum Bioinformatics-4 / [ed] Luigi Accardi , Wolfgang Freudenberg,, Masanori Ohya, World Scientific, 2011, p. 51-60Chapter in book (Refereed)
  • 6. Asano, M
    et al.
    Ohya, M
    Tanaka, Y
    Yamato, I
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-like paradigm from molecular biology to cognitive psychology.2011In: Quantum Interaction, Springer, 2011, p. 182-191Chapter in book (Refereed)
  • 7.
    Asano, Masanari
    et al.
    Tokuyama Coll, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    A quantum-like model of selection behavior2017In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 78, p. 2-12Article in journal (Refereed)
    Abstract [en]

    In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory. (C) 2016 Elsevier Inc. All rights reserved.

  • 8.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Quantum-like dynamics of decision-making2012In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 391, no 5, p. 2083-2099Article in journal (Refereed)
    Abstract [en]

    In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the "rational strategy" provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect ("irrationality" of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011)[55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker. (C) 2011 Elsevier B.V. All rights reserved.

  • 9.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Quantum-like Dynamics of Decision-making in Prisoner's Dilemma Game2012In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1424, p. 453-457Article in journal (Refereed)
    Abstract [en]

    In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.

  • 10.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, I.
    Tokyo University of Science.
    Lamarckian Evolution of Epigenome from Open Quantum Systems and Entanglement2014In: Quantum Interaction: 7th International Conference, QI 2013, Leicester, UK, July 25-27, 2013. Selected Papers / [ed] Harald Atmanspacher, Emmanuel Haven, Kirsty Kitto, Derek Raine, Springer, 2014, p. 324-334Conference paper (Refereed)
    Abstract [en]

    We develop a quantum-like (QL) model of cellular evolution based on the theory of open quantum systems and entanglement between epigenetic markers in a cell. This approach is applied to modeling of epigenetic evolution of cellular populations. We point out that recently experimental genetics discovered numerous phenomena of cellular evolution adaptive to the pressure of the environment. In such phenomena epigenetic changes are fixed in one generation and, hence, the Darwinian natural selection model cannot be applied. A number of prominent genetists stress the Lamarckian character of epigenetic evolution. In quantum physics the dynamics of the state of a system (e.g. electron) contacting with an environment (bath) is described by the theory of open quantum systems. Therefore it is natural to apply this theory to model adaptive changes in the epigenome. Since evolution of the Lamarckian type is very rapid – changes in the epigenome have to be inherited in one generation – we have to find a proper mathematical description of such a speed up. In our model this is the entanglement of different epigenetic markers.

  • 11.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    A model of epigenetic evolution based on theory of open quantum systems2013In: Systems and Synthetic Biology, ISSN 1872-5325, Vol. 7, no 4, p. 161-173Article in journal (Refereed)
    Abstract [en]

    We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.

  • 12. Asano, Masanari
    et al.
    Basieva, Irina
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Yamato, Ichiro
    Quantum Information Biology2016In: Contextuality from Quantum Physics to Psychology / [ed] Ehtibar Dzhafarov, Scott Jordan, Ru Zhang, Victor Cervantes, World Scientific, 2016, p. 399-413Chapter in book (Refereed)
    Abstract [en]

    This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB reflects the two fundamental principles: a) adaptivity; and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.

  • 13.
    Asano, Masanari
    et al.
    Tokuyama Coll Technol, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology2015In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 10, p. 1362-1378Article in journal (Refereed)
    Abstract [en]

    We discuss foundational issues of quantum information biology (QIB)-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 (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism- quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems.

  • 14.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Quantum-like model of diauxie in Escherichia coli: operational description of precultivation effect2012In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 314, p. 130-137Article in journal (Refereed)
    Abstract [en]

    In this paper we apply the quantum-like (QL) approach to microbiology to present an operational description of the complex process of diauxie in Escherichia coil. We take as guaranteed that dynamics in cells is adaptive, i.e., it depends crucially on the microbiological context. This very general assumption is sufficient to appeal to quantum and more general QL probabilistic models. The next step is to find the operational representation - by operators in complex Hilbert space (as in quantum physics). To determine QL operators, we used the statistical data from Inada et al. (1996). To improve the QL-representation, we needed better experimental data. Corresponding experiments were recently done by two of the authors and in this paper we use these new data. In these data we found that biochemical context of precultivation of populations of E. coli plays a crucial role in E. coli preferences with respect to sugars. Hence, the form of the QL operator representing lactose operon activation also depends crucially on precultivation. One of our results is decomposition of the lactose operon activation operator to extract the factor determined by precultivation. The QL operational approach developed in this paper can be used not only for description of the process of diauxie in E. coli, but also other processes of gene expression. However, new experimental statistical data are demanded. (C) 2012 Elsevier Ltd. All rights reserved.

  • 15.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Quantum-like model of glucose effect on Escherichia coli growth2012In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1424, p. 507-512Article in journal (Refereed)
    Abstract [en]

    Recently, we proposed a new method to compute probabilities which do not satisfy basic law in classical probability theory. In this note, we analyze glucose effect in Escherichia coli's growth with the method, and we show an invariant quantity which Escherichia coli has.

  • 16.
    Asano, Masanari
    et al.
    Tokyo University of Science.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Non-Kolmogorovian approach to the context-dependent systems breaking the classical probability law.2013In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 43, no 7, p. 895-911Article in journal (Refereed)
    Abstract [en]

    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 and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

  • 17.
    Asano, Masanari
    et al.
    Tokyo University of Science .
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohyna, Masanori
    Tokyo University of Science.
    Tanaka, Yoshiharu
    Tokyo University of Science.
    Yamato, Ichiro
    Tokyo University of Science.
    Towards Modeling of Epigenetic Evolution with the Aid of Theory of Open Quantum Systems2012In: Quantum Theory: Reconsideration of Fundations 6 / [ed] Khrennikov, A; Atmanspacher, H; Migdall, A; Polyakov, S, American Institute of Physics (AIP), 2012, volume 1508, p. 75-78Conference paper (Refereed)
    Abstract [en]

    We apply theory of open quantum systems to modeling of epigenetic evolution. This is an attempt to unify Darwinian and Lamarckian viewpoints on evolution on the basis of a quantum-like model. The state of uncertainty of cell's epigenome is resolved to a stable and inherited epigenetic configuration. This process of evolution and stabilization is described by the quantum master equation (the Gorini-Kossakowski-Sudarshan-Lindblad equation). The initial state of epigenome starting interaction with a new environment is represented as a pure quantum state. It evolves to a steady state solution of the quantum master equation given by a diagonal density matrix. The latter represents the state resulting from a series of epimutations induced by the environment. We use the information interpretation of the wave function which was elaborated by C. Fuchs and A. Zeilinger.

  • 18.
    Asano, Masanari
    et al.
    Natl Inst Technol, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics. Natl Res Univ Informat Technol Mech & Opt ITMO, Russia.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    A model of differentiation in quantum bioinformatics2017In: Progress in Biophysics and Molecular Biology, ISSN 0079-6107, E-ISSN 1873-1732, Vol. 130, p. 88-98Article, review/survey (Refereed)
    Abstract [en]

    Differentiation is a universal process found in various phenomena of nature. As seen in the example of cell differentiation, the creation diversity on individual's character is caused by environmental interactions. In this paper, we try to explain its mechanism, which has been discussed mainly in Biology, by using the formalism of quantum physics. Our approach known as quantum bioinformatics shows that the temporal change of statistical state called decoherence fits to describe non-local phenomena like differentiation. (C) 2017 Elsevier Ltd. All rights reserved.

  • 19. Asano, Masanari
    et al.
    Masanori, Ohya
    Tanaka, Yoshiharu
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-like model of brain's functioning: Decision making from decoherence2011In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 281, no 1, p. 56-64Article in journal (Refereed)
  • 20. Asano, Masanari
    et al.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    On application of Gorini-Kossakowski-Sudarshan-Lindblad equation in cognitive psychology.2011In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 18, no 1, p. 55-69Article in journal (Refereed)
  • 21. Asano, Masanori
    et al.
    Ohya, Masanori
    Tanaka, Yoshiharu
    Yamato, Ichiro
    Basieva, Irina
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    A Mathematical Treatment of Joint and Conditional Probability2013In: Quantum Bio-Informatics V - Proceedings of the Quantum Bio-Informatics 2011: Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Accardi Luigi et al., World Scientific, 2013, p. 69-84Conference paper (Refereed)
  • 22.
    Basiev, T. T.
    et al.
    Institute of physics, Moscow.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Cooperative luminescence quenching on many-particle acceptors in disordered media2012In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 391, no 12, p. 3526-3532Article in journal (Refereed)
    Abstract [en]

    Many-body cooperative energy transfer is an important process in biology, medicine, photosynthesis, rare-earth-doped laser materials, responsible for up- and down-conversion of energy, optical excitation sensitization and relaxation. We present an analytical solution for long-time asymptotic of static luminescence quenching kinetics due to cooperative energy transfer to ensembles of acceptors comprised of two-, three-, and more particles. For cooperative energy transfer and cooperative luminescence quenching to n-body acceptors we have discovered a new law of power d/(nS - (n - 1)d) time dependence (d = 1, 2, 3 is the space dimension, S = 6, 8, 10 is the multipolarty of interaction: dipole-dipole, dipole-quadrupole, or quadrupole-quadrupole). The detailed numerical simulation of cooperative quenching by Monte-Carlo method confirms the theoretical result. (C) 2012 Elsevier B.V. All rights reserved.

  • 23. Basiev, T. T.
    et al.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Doroshenko, M. E.
    Luminescent nanophotonics and advanced solid state lasers2013In: Journal of Luminescence, ISSN 0022-2313, E-ISSN 1872-7883, Vol. 133, p. 233-243Article in journal (Refereed)
    Abstract [en]

    In this review, authors present their latest findings in luminescence quenching kinetics theory and advanced solid state laser experiments. Luminescence quenching kinetics is a popular and exceptionally useful tool to analyze the nanosized luminophores and laser material nanostructure. Quenching kinetics may be multistage, some stages having a complex, not exponential, form. It is often the case for modern laser materials, which are nanostructurized, and for particular cases of energy transfer (such as cooperative down-conversion). We present compact and easy-to-use analytical expressions and computer simulation for various cases of nonexponential quenching kinetics: migration-accelerated quenching in bulk material; cooperative luminescence quenching in bulk material; and two extreme cases of energy transfer in nanoparticles - static and with superfast migration (both including cooperative case of luminescence quenching in ensembles of acceptors comprised of two-, three-, and more particles). We also review the most perspective laser experiments lately performed in our laboratory, including those on fluoride laser nanoceramics and materials for middle infra-red lasers. (c) 2011 Elsevier B.V. All rights reserved.

  • 24. Basiev, T T
    et al.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Doroshenko, M E
    Luminescent nanophotonics, fluoride laser ceramics, and crystals2011In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 54, no 12, p. Article ID 1262-Article in journal (Refereed)
  • 25.
    Basiev, T. T.
    et al.
    A.M. Prokhorov General Physics Institute of RAS, Russia.
    Basieva, Irina
    A.M. Prokhorov General Physics Institute of RAS, Russia.
    Kornienko, A. A.
    Vitebsk State Technological University, Russia.
    Osiko, V. V.
    A.M. Prokhorov General Physics Institute of RAS, Russia.
    Pukhov, K. K.
    A.M. Prokhorov General Physics Institute of RAS, Russia.
    Sekatskii, S. K.
    Ecole Polytechnique Federale de Lausanne, Switzerland.
    Pre-selection of optical transitions in rare-earth ions in crystals perspective for quantum information processing2012In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 59, no 2, p. 166-178Article in journal (Refereed)
    Abstract [en]

    A systematic analysis of decoherence rates due to electron-phonon interactions for optical transitions of rare-earth dopant ions in crystals is presented in the frame of the point charge model. For this model, the large value of any one of the matrix elements of the unit tensor operator U((k)) of rank k for transitions within the 4f-electronic configuration, viz. U2, U4 or U6, is enough to ensure the strong optical transition between different levels, while the Stark-Stark transitions within the multiplet can be characterized by the matrix element U2 alone, the influence of elements U4, U6 being of much smaller order of magnitude and neglected. The circumstance that exactly such Stark-Stark transitions within the multiplet define the efficiency of electron-phonon interaction and, consequently, the decoherence rate (except for the case of lowest, less than approximately 2-4 K, temperatures), enables selection of optical transitions which are strong enough and at the same time are characterized by relatively small decoherence rates. Correspondingly, these optical transitions, provided that they lie in an appropriate spectral range and the gap to the nearest neighboring energy level is large enough (>500 cm(-1)) to prevent eventual fast phonon-assisted relaxation, should be considered as prospective for subsequent use in quantum informatics processing and communication. The list of such pre-selected transitions is given; the applicability area and limitations of our approach are discussed.

  • 26.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Entangled state preparation in clusters of three resonantly interacting fluorescent particles.2011In: Quantum Bio-Informatics V: Proceedings of the Quantum Bio-Informatics 2011, Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, Singapore: World Scientific, 2011, vol. 30, p. 85-94Conference paper (Refereed)
  • 27.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Entangled states preparation in clusters of three resonantly interacting fluorescent particles2013In: Quantum Probability Series QP-PQ, ISSN 1793-5121, Vol. 30, p. 85-94Article in journal (Refereed)
    Abstract [en]

    Quantum dynamics of the states of three resonantly interacting two-level fluorescent particles is considered. It is shown that resonant laser excitation may lead to state inversion and to entanglement of energy states of the particles. The exact analytical solution of the problem in the case of zero decoherence is given. It describes complex dynamics in the case of strong laser radiation as well as easier and more perspective for practical implementation case of weak laser field. For the latter situation, the approximate solution obtained by the perturbation theory application is also presented and tested against the exact theoretical solution and numerical simulation.

  • 28.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Theoretical method for states dynamics and entanglement optimization in bichromatically driven clusters of two and four resonantly interacting particles2013In: Journal of the Optical Society of America. B, Optical physics, ISSN 0740-3224, E-ISSN 1520-8540, Vol. 30, no 7, p. 1804-1814Article in journal (Refereed)
    Abstract [en]

    Bichromatic laser pumping is an effective tool to control (e. g., to drive into an entangled state) solid-state quantum bits of different nature. For clusters of resonantly interacting ions under bichromatic laser pumping, we present a theoretical approach and approximate analytical solution for quantum states dynamics. The solution provides an optimal ratio of laser pulse intensities needed for creating the maximally entangled states and performing quantum gates. Numerical simulation corroborates the analytical results. (C) 2013 Optical Society of America

  • 29.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. RAS, Moscow, Russia.
    Basiev, T. T.
    RAS, Moscow, Russia.
    Static cooperative luminescence quenching in nanoparticles2014In: Journal of Luminescence, ISSN 0022-2313, E-ISSN 1872-7883, Vol. 151, p. 88-92Article in journal (Refereed)
    Abstract [en]

    In nanoparticles (NPs) static quenching of luminescence may be slower than in bulk media due to the space restrictions on acceptor location. Many-body cooperative quenching (manifesting itself as, e.g., down-conversion) occurs when the donor energy is transferred to two-, three-, or more particles (a cooperative acceptor) at once. Random distribution of acceptor particles in diluted media accounts for the non-exponential form of the kinetics. When the analytical expression for the kinetics form is known, it can be fitted to the experiment in order to find various micro- and macro-quenching parameters of the luminescent material. In this paper, we present an analytical law for cooperative quenching kinetics in NPs at longer time. Its clear and compact form reflects the fact that, on average, donors located on the surface of NPs are the last to decay having acceptors on one side only. We compared the resulting formula with the Monte-Carlo computer simulation, and they show good agreement. (C) 2014 Elsevier B.V. All rights reserved.

  • 30.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Complementarity of Mental Observables2014In: Topics in Cognitive Science, ISSN 1756-8757, E-ISSN 1756-8765, Vol. 6, no 1, p. 74-78Article in journal (Refereed)
    Abstract [en]

    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.

  • 31.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Decision-making and cognition modeling from the theory of mental instruments2017In: The Palgrave Handbook of Quantum Models in Social Science: Applications and Grand Challenges / [ed] Emmanuel Haven, Andrei Khrennikov, Palgrave Macmillan, 2017, p. 75-93Chapter in book (Other academic)
    Abstract [en]

    The authors present the theory of quantum measurements in a humanities friendly way. The most general process of decision-making is represented with the aid of the formalism of quantum apparatuses and instruments. This measurement formalism generalizes the standard one based on the von Neumann–Lüders projection postulate. Generalized quantum observables are mathematically represented as positive operator valued measures (POVMs) and state transformers resulting from the feedback of measurements to the states of systems that are given by quantum instruments. The quantum scheme of indirect measurements (a special realization of quantum instruments) is applied to model decision-making as resulting from the interaction between the belief and decision states. The authors analyze the specific features of quantum instruments which are important for cognitive and social applications. In particular, the state transformers given by quantum instruments are in general less invasive than the state projections. Thus quantum-like decision-making need not be viewed as a kind of state collapse.

  • 32.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Observables Generalizing Positive Operator Valued Measures2012In: QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS 6, American Institute of Physics (AIP), 2012, p. 94-97Conference paper (Refereed)
    Abstract [en]

    We discuss a generalization of POVM which is used in quantum-like modeling of mental processing.

  • 33.
    Basieva, Irina
    et al.
    Prokhorov Gen Phys Inst, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements2015In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 45, no 10, p. 1379-1393Article in journal (Refereed)
    Abstract [en]

    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 (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility () (the standard perfect repeatability) 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 after the other. The second one, , is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

  • 34.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Russian Acad Sci, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Quantum(-like) Formalization of Common Knowledge: Binmore-Brandenburger Operator Approach2015In: Quantum Interaction (QI 2014): 8th International Conference, QI 2014, Filzbach, Switzerland, June 30 - July 3, 2014. Revised Selected Papers / [ed] Harald Atmanspacher, Claudia Bergomi , Thomas Filk, Kirsty Kitto, Springer, 2015, Vol. 8951, p. 93-104Conference paper (Refereed)
    Abstract [en]

    We present the detailed account of the quantum(-like) viewpoint to common knowledge. The Binmore-Brandenburger operator approach to the notion of common knowledge is extended to the quantum case. We develop a special quantum(-like) model of common knowledge based on information representations of agents which can be operationally represented by Hermitian operators. For simplicity, we assume that each agent constructs her/his information representation by using just one operator. However, different agents use in general representations based on noncommuting operators, i.e., incompatible representations. The quantum analog of basic system of common knowledge features K1 - K5 is derived.

  • 35.
    Basieva, Irina
    et al.
    City University of London, UK.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Testing Boundaries of Applicability of Quantum Probabilistic Formalism to Modeling of Cognition: Metaphors of Two and Three Slit Experiments2017In: QUANTUM INTERACTION, QI 2016 / [ed] DeBarros, JA; Coecke, B; Pothos, E, Springer, 2017, p. 49-56Conference paper (Refereed)
    Abstract [en]

    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.

  • 36. Basieva, Irina
    et al.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Asano, Masanari
    Ohya, Masanori
    Tanaka, Yoshiharu
    Dynamics of Entropy in Quantum-like Model of Decision Making.2011In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1327, p. 63-70Article in journal (Refereed)
    Abstract [en]

    We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)

  • 37.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Ohya, Masanori
    Yamato, Ichiro
    Quantum-like interference effect in gene expression: glucose-lactose destructive interference2011In: Systems and Synthetic Biology, ISSN 1872-5325, Vol. 5, no 1, p. 56-64Article in journal (Refereed)
  • 38.
    Basieva, Irina
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pothos, Emmanuel
    City University London, UK.
    Trueblood, Jennifer
    Vanderbilt University, USA.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Busemeyer, Jerome
    Indiana University, USA.
    Quantum probability updating from zero priors (by-passing Cromwell's rule)2017In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 77, p. 58-69Article in journal (Refereed)
    Abstract [en]

    Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes' rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell's rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell's rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell's rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments. (C) 2016 Elsevier Inc. All rights reserved.

  • 39.
    Busemeyer, Jerome R.
    et al.
    Indiana Univ, USA.
    Wang, Zheng
    Ohio State Univ, USA.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Applying quantum principles to psychology2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T163, article id 014007Article in journal (Refereed)
    Abstract [en]

    This article starts out with a detailed example illustrating the utility of applying quantum probability to psychology. Then it describes several alternative mathematical methods for mapping fundamental quantum concepts (such as state preparation, measurement, state evolution) to fundamental psychological concepts (such as stimulus, response, information processing). For state preparation, we consider both pure states and densities with mixtures. For measurement, we consider projective measurements and positive operator valued measurements. The advantages and disadvantages of each method with respect to applications in psychology are discussed.

  • 40. Glushkov, N. A.
    et al.
    Basiev, T. T.
    Basieva, Irina
    Russian Acad Sci, Prokhorov Gen Phys Inst, Res Ctr Laser Mat & Technol, Moscow 119991, Russia.
    Kinetics of Ultrafast Migration-Accelerated Quenching in Nanoparticles2011In: JETP Letters: Journal of Experimental And Theoretical Physics Letters, ISSN 0021-3640, E-ISSN 1090-6487, Vol. 93, no 12, p. 697-700Article in journal (Refereed)
  • 41.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics. Prokhorov Gen Phys Inst, Moscow, Russia.
    Possibility to agree on disagree from quantum information and decision making2014In: Journal of mathematical psychology (Print), ISSN 0022-2496, E-ISSN 1096-0880, Vol. 62-63, p. 1-15Article in journal (Refereed)
    Abstract [en]

    The celebrated Aumann theorem states that if two agents have common priors, and their posteriors for a given event E are common knowledge, then their posteriors must be equal; agents with the same priors cannot agree to disagree. The aim of this note is to show that in some contexts agents using a quantum probability scheme for decision making can agree to disagree even if they have the common priors, and their posteriors for a given event E are common knowledge. We also point to sufficient conditions guaranteeing impossibility to agree on disagree even for agents using quantum(-like) rules in the process of decision making. A quantum(-like) analog of the knowledge operator is introduced; its basic properties can be formulated similarly to the properties of the classical knowledge operator defined in the set-theoretical approach to representation of the states of the world and events (Boolean logics). However, this analogy is just formal, since quantum and classical knowledge operators are endowed with very different assignments of truth values. A quantum(-like) model of common knowledge naturally generalizing the classical set-theoretic model is presented. We illustrate our approach by a few examples; in particular, on attempting to escape the agreement on disagree for two agents performing two different political opinion polls. We restrict our modeling to the case of information representation of an agent given by a single quantum question-observable (of the projection type). A scheme of extending of our model of knowledge/common knowledge to the case of information representation of an agent based on a few question-observables is also presented and possible pitfalls are discussed. (C) 2014 Elsevier Inc. All rights reserved.

  • 42.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Quantum Model for Psychological Measurements: From the Projection Postulate to Interference of Mental Observables Represented As Positive Operator Valued Measures2014In: NeuroQuantology, ISSN 1303-5150, Vol. 12, no 3, p. 324-336Article in journal (Refereed)
    Abstract [en]

    Recently foundational issues of applicability of the formalism of quantum mechanics (QM) to cognitive psychology, decision making, and psychophysics attracted a lot of interest. In particular, in (Khrennikov et al., 2014) the possibility to use of the projection postulate and representation of "mental observables" by Hermitian operators was discussed in very detail. The main conclusion of the recent discussions on the foundations of "quantum(-like) cognitive psychology" is that one has to be careful in determination of conditions of applicability of the projection postulate as a mathematical tool for description of measurements of observables represented by Hermitian operators. To represent some statistical experimental data (both physical and mental) in the quantum(-like) way, one has to use generalized quantum observables given by positive operator-valued measures (POVMs). This paper contains a brief review on POVMs which can be useful for newcomers to the field of quantum(-like) studies. Especially interesting for cognitive psychology is a variant of the formula of total probability (FTP) with the interference term derived for incompatible observables given by POVMs. We present an interpretation of the interference term from the psychological viewpoint. As was shown before, the appearance of such a term (perturbing classical FTP) plays the important role in cognitive psychology, e.g., recognition of ambiguous figures and the disjunction effect. The interference term for observables given by POVMs has much more complicated structure than the corresponding term for observables given by Hermitian operators. We elaborate cognitive interpretations of different components of the POVMs-interference term and apply our analysis to a quantum(-like) model of decision making.

  • 43.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics. Russian Acad Sci, Russia.
    Quantum(-Like) Decision Making: On Validity of the Aumann Theorem2015In: Quantum Interaction (QI 2014) / [ed] Harald Atmanspacher, Claudia Bergomi, Thomas Filk, Kirsty Kitto, Springer, 2015, p. 105-118Conference paper (Refereed)
    Abstract [en]

    Through set-theoretic formalization of the notion of common knowledge, Aumann proved that if two agents have the common priors, and their posteriors for a given event are common knowledge, then their posteriors must be equal. In this paper we investigate the problem of validity of this theorem in the framework of quantum(-like) decision making.

  • 44.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-like Representation of Bayesian Inference2011In: ADVANCES IN QUANTUM THEORY / [ed] G. Jaeger, A. Khrennikov, M. Schlosshauer, G. Weihs, Melville, NY: American Institute of Physics (AIP), 2011, p. 57-62Chapter in book (Refereed)
  • 45.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics. Russian Acad Sci, Prokhorov Gen Phys Inst, Moscow 119991, Russia.
    Quantum-state dynamics as linear representation of classical (nonlinear) stochastic dynamics2014In: Journal of Russian Laser Research, ISSN 1071-2836, E-ISSN 1573-8760, Vol. 35, no 1, p. 71-78Article in journal (Refereed)
    Abstract [en]

    We show that the basic equation of the theory of open systems, the Gorini-Kossakowski-Sudarshan-Lindblad equation, as well as its linear and nonlinear generalizations have a natural classical probabilistic interpretation - within the framework of prequantum classical statistical field theory. The latter gives an example of the classical probabilistic model (with random fields as subquantum variables) reproducing the basic probabilistic predictions of quantum mechanics.

  • 46.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Dzhafarov, Ehtibar N.
    Purdue University, USA.
    Busemeyer, Jerome R.
    Indiana University, USA.
    Quantum Models for Psychological Measurements: An Unsolved Problem2014In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, no 10, article id e110909Article in journal (Refereed)
    Abstract [en]

    There has been a strong recent interest in applying quantum theory (QT) outside physics, including in cognitive science. We analyze the applicability of QT to two basic properties in opinion polling. The first property (response replicability) is that, for a large class of questions, a response to a given question is expected to be repeated if the question is posed again, irrespective of whether another question is asked and answered in between. The second property (question order effect) is that the response probabilities frequently depend on the order in which the questions are asked. Whenever these two properties occur together, it poses a problem for QT. The conventional QT with Hermitian operators can handle response replicability, but only in the way incompatible with the question order effect. In the generalization of QT known as theory of positive-operator-valued measures (POVMs), in order to account for response replicability, the POVMs involved must be conventional operators. Although these problems are not unique to QT and also challenge conventional cognitive theories, they stand out as important unresolved problems for the application of QT to cognition. Either some new principles are needed to determine the bounds of applicability of QT to cognition, or quantum formalisms more general than POVMs are needed.

  • 47.
    Khrennikov, Andrei
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ramelow, Sven
    Univ Vienna, Vienna, Austria ; Cornell Univ, Ithaca, USA .
    Ursin, Rupert
    Austrian Acad Sci, Vienna, Austria.
    Wittmann, Bernhard
    Austrian Acad Sci, Vienna, Austria ; Univ Vienna, Vienna, Austria .
    Kofler, Johannes
    Max Planck Inst Quantum Opt MPQ, Garching, Germany.
    Basieva, Irina
    Prokhorov Gen Phys Inst, Moscow, Russia.
    On the equivalence of the Clauser-Horne and Eberhard inequality based tests2014In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T163, article id 014019Article in journal (Refereed)
    Abstract [en]

    Recently, the results of the first experimental test for entangled photons closing the detection loophole (also referred to as the fair sampling loophole) were published (Vienna, 2013). From the theoretical viewpoint the main distinguishing feature of this long-aspired to experiment was that the Eberhard inequality was used. Almost simultaneously another experiment closing this loophole was performed (Urbana-Champaign, 2013) and it was based on the Clauser-Horne inequality (for probabilities). The aim of this note is to analyze the mathematical and experimental equivalence of tests based on the Eberhard inequality and various forms of the Clauser-Horne inequality. The structure of the mathematical equivalence is nontrivial. In particular, it is necessary to distinguish between algebraic and statistical equivalence. Although the tests based on these inequalities are algebraically equivalent, they need not be equivalent statistically, i.e., theoretically the level of statistical significance can drop under transition from one test to another (at least for finite samples). Nevertheless, the data collected in the Vienna test implies not only a statistically significant violation of the Eberhard inequality, but also of the Clauser-Horne inequality (in the ratio-rate form): for both a violation > 60 sigma.

  • 48.
    Nyman, Peter
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Quantum-like representation algorithm for trichotomous observables.2011In: International journal of theoretical physics, ISSN 0020-7748, E-ISSN 1572-9575, Vol. 50, no 12, p. 3864-3881Article in journal (Refereed)
    Abstract [en]

    We study the problem of representing statistical data (of any origin) by a complex probability amplitude. This paper is devoted to representation of data collected from measurements of two trichotomous observables. The complexity of the problem eventually increases compared to the case of dichotomous observables. We see that only special statistical data (satisfying a number of nonlinear constraints) have the quantum–like representation.

  • 49.
    Nyman, Peter
    et al.
    Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
    Basieva, Irina
    Representation of probabilistic data by complex probability amplitudes: the case of triple-valued observables.2010In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1327, p. 439-449Article in journal (Refereed)
    Abstract [en]

    The problem of inter-relation between classical and quantum probabilistic data wasdiscussed in numerous papers (from various points of view), see, e.g., [1, 2, 3, 4, 6, 5, 7,8, 14, 15]. We are interested in the problem of representation of probabilistic data of anyorigin 1 by complex probability amplitude, so to say a “wave function”. This problemwas discussed in very detail in [17]. A general QL-representation algorithm (QLRA)was presented in [17]. This algorithm is based on the formula of total probability withinterference term – a disturbance of the standard formula of total probability. Startingwith experimental probabilistic data, QLRA produces a complex probability amplitudesuch that probability can be reconstructed by using Born’s rule.Although the formal scheme of QLRA works for multi-valued observables of anarbitrary dimension, the description of the class of probabilistic data which can betransfered into QL-amplitudes (the domain of application of QLRA) depends very muchon the dimension. In [19] the simplest case of data generated by dichotomous observableswas studied. In this paper we study trichotomous observables. The complexity of theproblem increases incredibly comparing with the two dimensional case.Finally, we remark that our study is closely related to the triple slit interferenceexperiment and Sorkin’s equality [16]. This experiment provides an important test offoundations of QM.The scheme of presentation is the following one. We start with observables given byQM and derive constraints on phases which are necessary and sufficient for the QLrepresentation.Then we use these constraints to produce complex amplitudes from data(of any origin); some examples, including numerical, are given.

1 - 49 of 49
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