| 1. |
- Accardi, Luigi, et al.
(author)
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Application of Non-Kolmogorovian Probability and Quantum Adaptive Dynamics to Unconscious Inference in Visual Perception Process
- 2016
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In: Open systems & information dynamics. - 1230-1612 .- 1573-1324. ; 23:2
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Journal article (peer-reviewed)abstract
- Recently a novel quantum information formalism - quantum adaptive dynamics - was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantum adaptive dynamics describes mutual adapting of the information states of two interacting systems (physical or biological) as well as adapting of co-observations performed by the systems. In this paper we apply this formalism to model unconscious inference: the process of transition from sensation to perception. The paper combines theory and experiment. Statistical data collected in an experimental study on recognition of a particular ambiguous figure, the Schroer stairs, support the viability of the quantum(-like) model of unconscious inference including modelling of biases generated by rotation-contexts. From the probabilistic point of view, we study (for concrete experimental data) the problem of contextuality of probability, its dependence on experimental contexts. Mathematically contextuality leads to non-Komogorovness: probability distributions generated by various rotation contexts cannot be treated in the Kolmogorovian framework. At the same time they can be embedded in a "big Kolmogorov space" as conditional probabilities. However, such a Kolmogorov space has too complex structure and the operational quantum formalism in the form of quantum adaptive dynamics simplifies the modelling essentially.
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| 2. |
- Accardi, Luigi, et al.
(author)
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Quantum Markov Model for Data from Shafir-Tversky Experiments in Cognitive Psychology
- 2009
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In: Open systems & information dynamics. - Singapore : WSP. - 1230-1612 .- 1573-1324. ; 16:4, s. 371-385
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Journal article (peer-reviewed)abstract
- We analyze, from the point of view of quantum probability, statistical data from two interesting experiments, done by Shafir and Tversky [1, 2] in the domain of cognitive psychology. These are gambling experiments of Prisoner Dilemma type. They have important consequences for economics, especially for the justification of the Savage "Sure Thing Principle" [3] (implying that agents of the market behave rationally). Data from these experiments were astonishing, both from the viewpoint of cognitive psychology and economics and probability theory. Players behaved irrationally. Moreover, all attempts to generate these data by using classical Markov model were unsuccessful. In this note we show (by inventing a simple statistical test — generalized detailed balance condition) that these data are non-Kolmogorovian. We also show that it is neither quantum (i.e., it cannot be described by Dirac-von Neumann model). We proceed towards a quantum Markov model for these data.
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| 3. |
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| 4. |
- Basieva, Irina, 1974-, et al.
(author)
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"What Is Life?" : Open Quantum Systems Approach
- 2022
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In: Open systems & information dynamics. - : World Scientific. - 1230-1612 .- 1573-1324. ; 29:4
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Journal article (peer-reviewed)abstract
- Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modelling. In this paper, we turn to the famous Schrodinger's book "What is life?" and reformulate his speculations in terms of this theory. Schrodinger pointed to order preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrodinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preserve the order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment E: 1) entropy (disorder) increasing in the process of adaptation to the specific features of E; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.
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| 5. |
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| 6. |
- Bengtsson, Ingemar, et al.
(author)
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The Frame Potential, On Average
- 2009
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In: Open systems & information dynamics. - 1230-1612 .- 1573-1324. ; 16:2-3, s. 145-156
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Journal article (peer-reviewed)abstract
- A Symmetric Informationally Complete Positive Operator Valued Measure (SIC) consists of N-2 equiangular unit vectors in an N dimensional Hilbert space. The frame potential is a function of N-2 unit vectors. It has a unique global minimum if the vectors form a SIC, and this property has been made use of in numerical searches for SICs. When the vectors form an orbit of the Weyl-Heisenberg group the frame potential becomes a function of a single fiducial vector. We analytically compute the average of this function over Hilbert space. We also compute averages when the financial vector is placed in certain special subspaces defined by the Clifford group.
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| 7. |
- Chruściński, Dariusz, et al.
(author)
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Exposed Positive Maps in M4(ℂ)
- 2012
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In: Open systems & information dynamics. - 1230-1612 .- 1573-1324. ; 19:3
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Journal article (peer-reviewed)abstract
- It is shown that the family of so-called Breuer-Hall maps in M-4(C) possesses strong spanning property and hence they are exposed in the convex cone of positive maps in M-4(C).
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| 8. |
- Heydari, Hoshang
(author)
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Quantum Gate Entangler and Entangling Capacity of a General Multipartite Quantum System
- 2008
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In: Open systems & information dynamics. - 1230-1612 .- 1573-1324. ; 15:3, s. 213-222
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Journal article (peer-reviewed)abstract
- We construct quantum gate entangler for general multipartite states based on the construction of complex projective varieties. We also discuss in detail the construction of quantum gate entangler for higher dimensional bipartite and multipartite quantum systems. Moreover, we construct and discuss entangling capacity of general multipartite quantum systems.
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| 9. |
- Heydari, Hoshang
(author)
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Selective Phase Rotation Quantum Gate Entangler
- 2009
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In: Open systems & information dynamics. - : world scientific publishing. - 1230-1612 .- 1573-1324. ; 16:4, s. 407-412
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Journal article (peer-reviewed)abstract
- We construct a quantum gate entangler for multi-qubit states based on a selective phase rotation transform. In particular, we establish a relation between the quantum integral transform and the quantum gate entangler in terms of universal controlled gates for multi-qubit states. Our result gives an effective way of constructing topological and geometrical quantum gate entanglers for multipartite quantum systems, which could also lead to a construction of geometrical quantum algorithms.
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| 10. |
- Khrennikov, Andrei
(author)
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Algorithm for Quantum-like Representation:Transformation of Probabilistic Data into Vectors on Bloch's Sphere.
- 2008
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In: Open systems & information dynamics. - : World Scientific Publ.. - 1230-1612 .- 1573-1324. ; 15:3, s. 223-230
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Journal article (peer-reviewed)abstract
- In this paper, we present a simple algorithm for representation of statis-tical data of any origin by complex probability amplitudes. Numerical simulation withMathematica-6 is performed, cf. [1] and [2] on recent numerical simulation for quantumcorrelations. The Bloch's sphere is used for the visualization of results of numerical sim-ulation. On the one hand, creation of such a quantum-like (QL) representation and itsnumerical approval is an important step in clari¯cation of extremely complicated inter-relation between classical and quantum randomness. On the other hand, it opens newpossibilities for applying the mathematical formalism of QM in other domains of science.
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