| 1. |
- Asano, Masanari, et al.
(författare)
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Non-Kolmogorovian approach to the context-dependent systems breaking the classical probability law.
- 2013
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 43:7, s. 895-911
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Asano, Masanari, et al.
(författare)
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Quantum Information Biology : From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology
- 2015
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 45:10, s. 1362-1378
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Asano, Masanari, et al.
(författare)
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Quantum-Like Model for Decision Making Process inTwo Players Game : A Non-Kolmogorovian Model
- 2011
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 41:3, s. 538-548
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Tidskriftsartikel (refereegranskat)abstract
- 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 classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).
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| 4. |
- Aurell, Erik, et al.
(författare)
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Quantum Black Holes as Solvents
- 2021
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Ingår i: Foundations of physics. - : Springer Nature. - 0015-9018 .- 1572-9516. ; 51:2
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Tidskriftsartikel (refereegranskat)abstract
- Almost all of the entropy in the universe is in the form of Bekenstein-Hawking (BH) entropy of super-massive black holes. This entropy, if it satisfies Boltzmann's equation S=log N, hence represents almost all the accessible phase space of the Universe, somehow associated to objects which themselves fill out a very small fraction of ordinary three-dimensional space. Although time scales are very long, it is believed that black holes will eventually evaporate by emitting Hawking radiation, which is thermal when counted mode by mode. A pure quantum state collapsing to a black hole will hence eventually re-emerge as a state with strictly positive entropy, which constitutes the famous black hole information paradox. Expanding on a remark by Hawking we posit that BH entropy is a thermodynamic entropy, which must be distinguished from information-theoretic entropy. The paradox can then be explained by information return in Hawking radiation. The novel perspective advanced here is that if BH entropy counts the number of accessible physical states in a quantum black hole, then the paradox can be seen as an instance of the fundamental problem of statistical mechanics. We suggest a specific analogy to the increase of the entropy in a solvation process. We further show that the huge phase volume (N), which must be made available to the universe in a gravitational collapse, cannot originate from the entanglement between ordinary matter and/or radiation inside and outside the black hole. We argue that, instead, the quantum degrees of freedom of the gravitational field must get activated near the singularity, resulting in a final state of the 'entangled entanglement' form involving both matter and gravity.
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| 5. |
- Badziag, Piotr, et al.
(författare)
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Pentagrams and Paradoxes
- 2011
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Ingår i: FOUNDATIONS OF PHYSICS. - : Springer Science Business Media. - 0015-9018 .- 1572-9516. ; 41:3, s. 414-423
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Tidskriftsartikel (refereegranskat)abstract
- Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum "paradoxes", such as that of Hardy.
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| 6. |
- Basieva, Irina, 1974-, et al.
(författare)
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On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements
- 2015
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 45:10, s. 1379-1393
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
- Bengtsson, Ingemar, et al.
(författare)
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Preface
- 2011
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 41:3, s. 281-281
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 8. |
- Bengtsson, Ingemar, et al.
(författare)
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Preface
- 2011
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 41:3, s. 281-281
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Tidskriftsartikel (refereegranskat)
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| 9. |
- Bengtsson, Ingemar, 1957-
(författare)
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SICs: Some explanations
- 2020
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 50:12, s. 1794-1808
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Tidskriftsartikel (refereegranskat)abstract
- The problem of constructing maximal equiangular tight frames or SICs was raised by Zauner in 1998. Four years ago it was realized that the problem is closely connected to a major open problem in number theory. We discuss why such a connection was perhaps to be expected, and give a simplified sketch of some developments that have taken place in the past 4 years. The aim, so far unfulfilled, is to prove existence of SICs in an infinite sequence of dimensions.
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| 10. |
- Bengtsson, Ingemar
(författare)
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The Number Behind the Simplest SIC-POVM
- 2017
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Ingår i: Foundations of physics. - : Springer Science and Business Media LLC. - 0015-9018 .- 1572-9516. ; 47:8, s. 1031-1041
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Tidskriftsartikel (refereegranskat)abstract
- The simple concept of a SIC poses a very deep problem in algebraic number theory, as soon as the dimension of Hilbert space exceeds three. A detailed description of the simplest possible example is given.
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