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Andrei Khrennikov

Publications and source records attributed to Andrei Khrennikov.

At least 55 records · Page 3Linked to original sources

Social laser model for the Bandwagon effect: generation of coherent information waves

During the last years our society was often exposed to the coherent information waves of high amplitudes. These are waves of huge social energy. Often they are of the destructive character, a kind of information tsunami. But, they can carry as well positive improvements in the human society, as waves of decision making matching rational recommendations of societal institutes. The main distinguishing features of these waves are their high amplitude, coherence (homogeneous character of social actions generated by them), and short time needed for their generation and relaxation. Such waves can be treated as large scale exhibition of the Bandwagon effect. We show that this socio-psychic phenomenon can be modeled on the basis of the recently developed {\it social laser theory}. This theory can be used to model {\it stimulated amplification of coherent social actions}. "Actions" are treated very generally, from mass protests to votes and other collective decisions, as, e.g., acceptance (often unconscious) of some societal recommendations. In this paper, we concentrate on theory of laser resonators, physical vs. social. For the latter, we analyze in very detail functioning of the internet based Echo-Chambers. Their main purpose is increasing of the power of the quantum information field as well as its coherence. Of course, the Bandwagon effect is well known and well studied in social psychology. However, the social laser theory gives the possibility to model it by using the general formalism of quantum field theory. The paper contains minimum of mathematics and it can be readable by researchers working in psychology, cognitive, social, and political sciences; it might also be interesting for experts in information theory and artificial intelligence.

physics.soc-ph↗

Quantum postulate vs. quantum nonlocality: Is Devil in h?

This note is a part of my efforts for getting rid of nonlocality from quantum mechanics (QM). Quantum nonlocality is two faced Janus, one face is Lüders projection nonlocality, another face is Bell nonlocality. This paper is devoted to disillusion of the latter. The main casualty of Bell's model with hidden variables is that it straightforwardly contradicts to the Heinsenberg's uncertainty and generally Bohr's complementarity principles. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as it is. The original Einstein-Podolsky-Rosen (EPR) argument was based on the Heinseberg's principle, but EPR did not question it. Hence, the arguments of EPR and Bell differ crucially. It is worth to find the physical seed of the aforementioned principles. This is the {\it quantum postulate}: the existence of indivisible quantum of action. Bell's approach with hidden variable straightforwardly implies rejection of the quantum postulate. Heisenberg compared the quantum postulate with constancy of light's velocity in special relativity. Thus attempts to explain long distance correlations within the Bell model can be compared with attempts to construct models violating the laws of relativity theory. Following Zeilinger, I search for the fundamental principles of quantum mechanics (QM) similar to the principles of relativity and consider the quantum action and complementarity principles as such principles.

quant-ph↗

A comment on paper of Kim et al. on mechanisms of hysteresis in human brain networks: comparing with theoretical m-adic model

This comment is aimed to point out that the recent work due to Kim, et al. in which the clinical and experiential assessment of a brain network model suggests that asymmetry of synchronization suppression is the key mechanism of hysteresis has coupling with our theoretical hysteresis model of unconscious-conscious interconnection based on dynamics on m-adic trees.

q-bio.NC↗

Two faced Janus of quantum nonlocality

This paper is a new step towards getting rid of nonlocality from quantum physics. This is an attempt to structure the nonlocality mess. "Quantum nonlocality" is Janus faced. One its face is projection (Einstein-Lüders) nonlocality and another Bell nonlocality. The first one is genuine quantum nonlocality, the second one is subquantum nonlocality. Recently it was shown that Bell "nonlocality" is a simple consequence of the complementarity principle. We now show that projection nonlocality has no connection with physical space. Projection state update is generalization of the well known operation of probability update used in classical inference. We elevate the role of interpretations of a quantum state. By using the individual (physical) interpretation, one can really get the illusion of a spooky action at a distance resulting from Lüders' state update. The statistical interpretation combined with treating the quantum formalism as machinery for update of probability is known as the Växjö interpretation. Here one follows the standard scheme of probability update adjusted to the quantum calculus of probability. The latter is based on operating with states represented by vectors (or density operators). We present in parallel classical and quantum probability updates. From this presentation, it is clear that both classical and quantum "faster-than-light change of statistical correlation" take place in mental and not physical space.

quant-ph↗

Echoing the recent Google success: Foundational Roots of Quantum Supremacy

The recent Google's claim on breakthrough in quantum computing is a gong signal for further analysis of foundational roots of (possible) superiority of some quantum algorithms over the corresponding classical algorithms. This note is a step in this direction. We start with critical analysis of rather common reference to entanglement and quantum nonlocality as the basic sources of quantum superiority. We elevate the role of the Bohr's {\it principle of complementarity}\footnote{} (PCOM) by interpreting the Bell-experiments as statistical tests of this principle. (Our analysis also includes comparison of classical vs genuine quantum entanglements.) After a brief presentation of PCOM and endowing it with the information interpretation, we analyze its computational counterpart. The main implication of PCOM is that by using the quantum representation of probability, one need not compute the joint probability distribution (jpd) for observables involved in the process of computation. Jpd's calculation is exponentially time consuming. Consequently, classical probabilistic algorithms involving calculation of jpd for $n$ random variables can be over-performed by quantum algorithms (for big values of $n).$ Quantum algorithms are based on quantum probability calculus. It is crucial that the latter modifies the classical formula of total probability (FTP). Probability inference based on the quantum version of FTP leads to constructive interference of probabilities increasing probabilities of some events. We also stress the role the basic feature of the genuine quantum superposition comparing with the classical wave superposition: generation of discrete events in measurements on superposition states. Finally, the problem of superiority of quantum computations is coupled with the quantum measurement problem and linearity of dynamics of the quantum state update.

quant-ph↗

Quantum versus classical entanglement: eliminating the issue of quantum nonlocality

We analyze interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that "quantum nonlocality" is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of (semi-)classical field models in favor of quantum mechanics. Classical entanglement sources produce light beams with the coefficient of second order coherence $g^{(2)}(0) \geq 1.$ This feature of classical entanglement is obscured by using intensities of signals in different channels, instead of counting clicks of photo-detectors. Interplay between intensity and clicks counting is not just a technicality. We elevate this issue to the high foundational level.

quant-ph↗

Getting rid of nonlocality from quantum physics

This paper is aimed to dissociate nonlocality from quantum theory. We demonstrate that the tests on violation of the Bell type inequalities are simply statistical tests of local incompatibility of observables. In fact, these are tests on violation of {\it the Bohr complementarity principle.} Thus, the attempts to couple experimental violations of the Bell type inequalities with "quantum nonlocality" is really misleading. These violations are explained in the quantum theory as exhibitions of incompatibility of observables for a single quantum system, e.g., the spin projections for a single electron or the polarization projections for a single photon. Of course, one can go beyond quantum theory with the hidden variables models (as was suggested by Bell) and then discuss their possible nonlocal features. However, conventional quantum theory is local.

quant-ph↗

Generalized Fock space and contextuality

This paper is devoted to linear space representations of contextual probabilities - in generalized Fock space. This gives the possibility to use the calculus of creation and annihilation operators to express probabilistic dynamics in the Fock space (in particular, the wide class of classical kinetic equations). In this way we reproduce the Doi-Peliti formalism. The context-dependence of probabilities can be quantified with the aid of the generalized formula of total probability - by the magnitude of the interference term.

quant-ph↗

Violation of the Bell's type inequalities as a local expression of incompatibility

By filtering out the philosophic component we can be said that the EPR-paper was directed against the straightforward interpretation of the Heisenberg's uncertainty principle or more generally the Bohr's complementarity principle. The latter expresses contextuality of quantum measurements: dependence of measurement's output on the complete experimental arrangement. However, Bell restructured the EPR-argument against complementarity to justify nonlocal theories with hidden variables of the Bohmian mechanics' type. Then this Bell's kind of nonlocality - {\it subquantum nonlocality} - was lifted to the level of quantum theory - up to the terminology {\it "quantum nonlocality"}. The aim of this short note is to explain that Bell's test is simply a special {\it test of local incompatibility of quantum observables}, similar to interference experiments, e.g., the two-slit experiment.

quant-ph↗

Bohm-Bell type experiments: Classical probability approach to (no-)signaling and applications to quantum physics and psychology

We consider the problem of representation of quantum states and observables in the framework of classical probability theory (Kolmogorov's measure-theoretic axiomatics, 1933). Our aim is to show that, in spite of the common opinion, correlations of observables $A_1, A_2$ and $B_1,B_2$ involved in the experiments of the Bohm-Bell type can be expressed as correlations of classical random variables $a_1, a_2$ and $b_1, b_2.$ The crucial point is that correlations $\langle A_i, B_j \rangle$ should be treated as conditional on the selection of the pairs $(i, j).$ The setting selection procedure is based on two random generators $R_A$ and $R_B.$ They are also considered as observables, supplementary to the "basic observables" $A_1, A_2$ and $B_1, B_2.$ These observables are absent in the standard description, e.g., in the scheme for derivation of the CHSH-inequality. We represent them by classical random variables $r_a$ and $r_b.$ Following the recent works of Dzhafarov and collaborators, we apply our conditional correlation approach to characterize (no-)signaling in the classical probabilistic framework. Consideration the Bohm-Bell experimental scheme in the presence of signaling is important for applications outside quantum mechanics, e.g., in psychology and social science.

quant-ph↗

Has CHSH-inequality any relation to EPR-argument?

We emphasize the role of the precise correlations loophole in attempting to connect the CHSH type inequalities with the EPR-argument. The possibility to test theories with hidden variables experimentally by using such inequalities is questioned. The role of the original Bell inequality is highlighted. The interpretation of the CHSH inequality in the spirit of Bohr, as a new test of incompatibility, is presented. The positions of Bohr, Einstein, Podolsky, Rosen, Bell, Clauser, Horne, Shimony, Holt, De Broglie, Hertz, and Boltzmann on interrelation of theory and experiment are enlightened.

quant-ph↗

Hertz's viewpoint on quantum theory

In 19th century (in the process of transition from mechanics to the field theory) the German school of theoretical physics confronted problems similar to the basic problems in the foundations of quantum mechanics (QM). Hertz tried to resolve such problem through analysis of the notion of a scientific theory and interrelation of theory and experiment. This analysis led him to the Bild (image) conception of theory (which was latter essentially developed, but also modified by Boltzmann). In this paper we claim that to resolve the basic foundational problems of QM, one has to use the Bild conception and reject the observational viewpoint on physical theory. As an example of a Bild theory underlying QM (treated as an observational theory), we consider prequantum classical statistical field theory (PCSFT): theory of random subquantum fields.

quant-ph↗

Groups of automorphisms of p-adic integers and the problem of the existence of fully homomorphic ciphers

In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result of this paper is the description of groups of automorphisms of $p$-adic integers with one or two arithmetic or coordinate-wise logical operations on $p$-adic integers. To describe groups of automorphisms, we use the apparatus of the $p$-adic analysis and $p$-adic dynamical systems. The motive for the study of groups of automorphism of algebraic systems over $p$-adic integers is the question of the existence of a fully homomorphic encryption in a given family of ciphers. The relationship between these problems is based on the possibility of constructing a "continuous" $p$-adic model for some families of ciphers (in this context, these ciphers can be considered as "discrete" systems). As a consequence, we can apply the "continuous" methods of $p$-adic analysis to solve the "discrete" problem of the existence of fully homomorphic ciphers.

math.NT↗

Towards experiments to test violation of the original Bell inequality

The aim of this note is to attract attention of experimenters to the original Bell (OB) inequality which was shadowed by the common consideration of the CHSH inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the EPR-argumentation. And only this inequality is related to the EPR-Bohr debate. However, the last statement can be objected by some experts working in quantum foundations. Therefore to convince experimenters to perform the OB-violation experiment, we prefer to concentrate on the second distinguishing feature of the OB inequality which was emphasized by I. Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last years were characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing with very high probability the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of Hensen et al. experiment for entangled electrons.

quant-ph↗

Buonomano against Bell: Nonergodicity or nonlocality?

The aim of this note is to attract attention of the quantum foundational community to the fact that in Bell's arguments one can not distinguish two hypotheses: a) quantum mechanics is {\it nonlocal}, b) quantum mechanics is {\it nonergodic.} Therefore experimental violations of Bell's inequality can be as well interpreted as supporting the hypothesis that stochastic processes induced by quantum measurements are nonergodic. The latter hypothesis was discussed actively by Buonomano since 1980th. However, in contrast to Bell's hypothesis on nonlocality it did not attract so much attention. The only experiment testing the hypothesis on nonergodicity was performed in neutron interferometry (by Summhammer, in 1989). This experiment can be considered as rejecting this hypothesis. However, it cannot be considered as a decisive experiment. New experiments are badly needed. We point out that a nonergodic model can be realistic, i.e., the distribution of hidden (local!) variables is well defined. We also discuss coupling of violation of the Bell inequality with violation of the condition of weak mixing for ergodic dynamical systems.

quant-ph↗

Molecular recognition of the environment and mechanisms of the origin of species in quantum-like modeling of evolution

A review of the mechanisms of speciation is performed. The mechanisms of the evolution of species, taking into account the feedback of the state of the environment and mechanisms of the emergence of complexity, are considered. It is shown that these mechanisms, at the molecular level, cannot work steadily in terms of classical mechanics. Quantum mechanisms of changes in the genome, based on the long-range interaction potential between biologically important molecules, are proposed as one of possible explanation. Different variants of interactions of the organism and environment based on molecular recognition and leading to new species origins are considered. Experiments to verify the model are proposed. This bio-physical study is completed by the general operational model of based on quantum information theory. The latter is applied to model epigenetic evolution.

q-bio.PE↗

Energy flow in biological system: Bioenergy transduction of V1-ATPase molecular rotary motor from E. hirae

We classify research fields in biology into those on flows of materials, energy, and information. As a representative energy transducing machinery in biology, our research target, V1-ATPase from a bacterium Enterococcus hirae, a typical molecular rotary motor is introduced. Structures of several intermediates of the rotary motor are described and the molecular mechanism of the motor converting chemical energy into mechanical energy is discussed. Comments and considerations on the information flow in biology, especially on the thermodynamic entropy in quantum physical and biological systems, are added in a separate section containing the biologist friendly presentation of this complicated question.

q-bio.BM↗