Quantum-like Theory Research Articles

On the emergent “Quantum” theory in complex adaptive systems

We explore the concept of emergent quantum-like theory in complex adaptive systems, and examine in particular the concrete example of such an emergent (or “mock”) quantum theory in the Lotka–Volterra system. In general, we investigate the possibility of implementing the mathematical formalism of quantum mechanics on classical systems, and what would be the conditions for using such an approach. We start from a standard description of a classical system via Hamilton–Jacobi (HJ) equation and reduce it to an effective Schrodinger-type equation, with a (mock) Planck constant ▪ , which is system-dependent. The condition for this is that the so-called quantum potential VQ, which is state-dependent, is canceled out by some additional term in the HJ equation. We consider this additional term to provide for the coupling of the classical system under consideration to the ‘environment’. We assume that a classical system could cancel out the VQ term (at least approximately) by fine tuning to the environment. This might provide a mechanism for establishing a stable, stationary states in (complex) adaptive systems, such as biological systems. In particular, we present a general argument as to why the non-equilibrium dynamics of a classical system could lead to a mock quantum description that ensures stability compatible with adaptability. In this context we emphasize the state dependent nature of the mock quantum dynamics and we also introduce the new concept of the mock quantum, state dependent, statistical field theory. We also discuss some universal features of the quantum-to-classical as well as the mock-quantum-to-classical transition found in the turbulent phase of the hydrodynamic formulation of our proposal. In this way we re-frame the concept of decoherence into the concept of ‘quantum turbulence’, i.e. that the transition between quantum and classical could be defined in analogy to the transition from laminar to turbulent flow in hydrodynamics.

'The agency of observation not to be neglected': complementarity, causality and the arrow of events in quantum and quantum-like theories.

The argument of this article is grounded in the irreducible interference of observational instruments in our interactions with nature in quantum physics and, thus, in the constitution of quantum phenomena versus classical physics, where this interference can, in principle, be disregarded. The irreducible character of this interference was seen by N. Bohr as the principal distinction between classical and quantum physics and grounded his interpretation of quantum phenomena and quantum theory. Bohr saw complementarity as a generalization of the classical ideal of causality, which defined classical physics and relativity. While intimated by Bohr, the relationships among observational technology, complementarity, causality and the arrow of events (a new concept that replaces the arrow of time commonly used in this context) were not addressed by him either. The article introduces another new concept, that of quantum causality, as a form of probabilistic causality. The argument of the article is based on a particular interpretation of quantum phenomena and quantum theory, defined by the concept of 'reality without realism (RWR)'. This interpretation follows Bohr's interpretation but contains certain additional features, in particular the Dirac postulate. The article also considers quantum-like (Q-L) theories (based in the mathematics of QM) from the perspective it develops. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.

The No-Cloning Life: Uniqueness and Complementarity in Quantum and Quantum-like Theories.

This article considers a rarely discussed aspect, the no-cloning principle or postulate, recast as the uniqueness postulate, of the mathematical modeling known as quantum-like, Q-L, modeling (vs. classical-like, C-L, modeling, based in the mathematics adopted from classical physics) and the corresponding Q-L theories beyond physics. The principle is a transfer of the no-cloning principle (arising from the no-cloning theorem) in quantum mechanics (QM) to Q-L theories. My interest in this principle, to be related to several other key features of QM and Q-L theories, such as the irreducible role of observation, complementarity, and probabilistic causality, is connected to a more general question: What are the ontological and epistemological reasons for using Q-L models vs. C-L ones? I shall argue that adopting the uniqueness postulate is justified in Q-L theories and adds an important new motivation for doing so and a new venue for considering this question. In order to properly ground this argument, the article also offers a discussion along similar lines of QM, providing a new angle on Bohr's concept of complementarity via the uniqueness postulate.

On "Decisions and Revisions Which a Minute Will Reverse": Consciousness, The Unconscious and Mathematical Modeling of Thinking.

This article considers a partly philosophical question: What are the ontological and epistemological reasons for using quantum-like models or theories (models and theories based on the mathematical formalism of quantum theory) vs. classical-like ones (based on the mathematics of classical physics), in considering human thinking and decision making? This question is only partly philosophical because it also concerns the scientific understanding of the phenomena considered by the theories that use mathematical models of either type, just as in physics itself, where this question also arises as a physical question. This is because this question is in effect: What are the physical reasons for using, even if not requiring, these types of theories in considering quantum phenomena, which these theories predict fully in accord with the experiment? This is clearly also a physical, rather than only philosophical, question and so is, accordingly, the question of whether one needs classical-like or quantum-like theories or both (just as in physics we use both classical and quantum theories) in considering human thinking in psychology and related fields, such as decision science. It comes as no surprise that many of these reasons are parallel to those that are responsible for the use of QM and QFT in the case of quantum phenomena. Still, the corresponding situations should be understood and justified in terms of the phenomena considered, phenomena defined by human thinking, because there are important differences between these phenomena and quantum phenomena, which this article aims to address. In order to do so, this article will first consider quantum phenomena and quantum theory, before turning to human thinking and decision making, in addressing which it will also discuss two recent quantum-like approaches to human thinking, that by M. G. D’Ariano and F. Faggin and that by A. Khrennikov. Both approaches are ontological in the sense of offering representations, different in character in each approach, of human thinking by the formalism of quantum theory. Whether such a representation, as opposed to only predicting the outcomes of relevant experiments, is possible either in quantum theory or in quantum-like theories of human thinking is one of the questions addressed in this article. The philosophical position adopted in it is that it may not be possible to make this assumption, which, however, is not the same as saying that it is impossible. I designate this view as the reality-without-realism, RWR, view and in considering strictly mental processes as the ideality-without-idealism, IWI, view, in the second case in part following, but also moving beyond, I. Kant’s philosophy.

Phishing for (Quantum-Like) Phools—Theory and Experimental Evidence

Quantum-like decision theory is by now a theoretically well-developed field (see e.g., Danilov, Lambert-Mogiliansky & Vergopoulos, 2018). We provide a first test of the predictions of an application of this approach to persuasion. One remarkable result entails that, in contrast to Bayesian persuasion, distraction rather than relevant information has a powerful potential to influence decision-making. We first develop a quantum decision model of choice between two uncertain alternatives. We derive the impact of persuasion by means of distractive questions and contrast them with the predictions of the Bayesian model. Next, we provide the results from a first test of the theory. We conducted an experiment where respondents choose between supporting either one of two projects to save endangered species. We tested the impact of persuasion in the form of questions related to different aspects of the uncertain value of the two projects. The experiment involved 1253 respondents divided into three groups: a control group, a first treatment group and the distraction treatment group. Our main result is that, in accordance with the predictions of quantum persuasion but in violation with the Bayesian model, distraction significantly affects decision-making. Population variables play no role. Some significant variations between subgroups are exhibited and discussed. The results of the experiment provide support for the hypothesis that the manipulability of people’s decision-making can to some extent be explained by the quantum indeterminacy of their subjective representation of reality.

Quantum-like modelling in game theory: Quo Vadis? A brief review

Purpose The current paper is a brief review of the emerging field of quantum-like modelling in game theory. This paper aims to explore several quantum games, which are superior compared to their classical counterparts, which means either they give rise to superior Nash equilibria or they make the game fairer. For example, quantum Prisoners Dilemma generates Pareto superior outcomes as compared to defection outcome in the famous classical case. Again, a quantum-like version of cards game can make the game fairer, increasing the chance of winning of players who are disadvantaged in the classical case. This paper explores all the virtues of simple quantum games, also highlighting some findings of the authors as regards Prisoners Dilemma game. Design/methodology/approach As this is a general review paper, the authors have not demonstrated any specific mathematical method, rather explored the well-known quantum probability framework, used for designing quantum games. They have a short appendix which explores basic structure of Hilbert space representation of human decision-making. Findings Along with the review of the extant literature, the authors have also highlighted some new findings for quantum Prisoners Dilemma game. Specifically, they have shown in the earlier studies (which are referred to here) that a pure quantum entanglement set up is not needed for designing better games, even a weaker condition, which is classical entanglement is sufficient for producing Pareto improved outcomes. Research limitations/implications Theoretical research, with findings and implications for future game designs, it has been argued that it is not always needed to have true quantum entanglement for superior Nash Equilibria. Originality/value The main purpose here is to raise awareness mainly in the social science community about the possible applications of quantum-like game theory paradigm. The findings related to Prisoners Dilemma game are, however, original.

Naturalism and political science adaptation to the non-classical world picture

One of the greatest achievements of the humanity is obviously the recognition of the systematic unity of the natural and social knowledge. However, this recognition was not constant. The forming development and history of political sciences reflected it rather evidently, tending to go from one extreme to another - from identifying its methods with natural, to pretending for its uniqueness, or even universality. All these questions got a special importance in the perspective of the new non-classical world picture, but the adaptation of political sciences to a new type of thinking meets considerable difficulties. The analysis of the most significant approaches towards the political and international processes demonstrate, that the acceptance of the new postulates od none-classical and post-none-classical pictures of the world is quite complicated. Simultaneously with the preservation of the pure mechanistic, approach some of the elements of the new world pictures were taken from quantum physics, biology, as well as the chance factor and the rejection of the casual relationships. Nevertheless, it is better to speak not about the translation of the methods and approaches from natural sciences to political, but about the attempts to build “weak” theories or analogues (for instance, quantum-like theories). Nevertheless, generally speaking, political as well as other social sciences tend to be developing accepting the zeitgeist. The adaption of political sciences to the new world pictures is inevitable,, but would be limited by definition. Even with the backgrounds of the unity of knowledge as such, its methods and instruments are quite different and even during the process of adaption change so significantly and are so greatly reduced, that they preserve only names and imitation of the other sciences’ methodology. Anyway, we should follow the parallelcourse.

Naturalism and political science: adaptation to the non-classical world picture

Introduction. One of the greatest achievements of the humanity is obviously the recognition of the systematic unity of the natural and social knowledge. However, this recognition was not constant. The emergence, development and history of political sciences reflected it rather evidently, tending to go from one extreme to another – from identifying its methods with those of positive science to pretending to be unique or even universal. All these questions acquired special importance in the new non-classical world, but the adaptation of political sciences to a new type of thinking meets considerable difficulties.Methods of study. The main method of the study is comparative analysis of the variations to connect philosophical and substantive (ontological and epistemological) tools with political and applied ones of researching political and international political processes and phenomena. Moreover, the authors also used the interpretation approach.Results. The analysis of the most significant approaches towards the political and international processes demonstrate that the acceptance of the new postulates of non-classical and post-nonclassical pictures of the world is quite complicated. Simultaneously with the preservation of the pure mechanistic, approach some of the elements of the new world pictures were taken from quantum physics, biology. The chance factor and the rejection of the casual relationships were also taken into consideration. Nevertheless, it is better to speak not about the transfer of the methods and approaches from natural to political sciences, but about the attempts to build “weak” theories or analogues of theories (for instance, quantum-like theories). Nevertheless, generally speaking, political as well as other social sciences tend to be developing capturing the zeitgeist.Discussion and Conclusions. The adaptation of political sciences to new scientific pictures of the world is inevitable, but limited by definition: for all unity of knowledge as such, their methods and tools are very different and even undergo such significant changes and simplifications in the process of adaptation that they often retain only the names and imitations of the methodologies of other sciences. And yet, at least we have to go in parallel. But some caution here would not hurt at all.

Entropy of mixing exists only for classical and quantum-like theories among the regular polygon theories

The thermodynamical entropy of a system which consists of different kinds of ideal gases is known to be defined successfully in the case when the differences are described by classical or quantum theory. Since these theories are special examples in the framework of generalized probabilistic theories (GPTs), it is natural to generalize the notion of thermodynamical entropy to systems where the internal degrees of particles are described by other possible theories. In this paper, we consider thermodynamical entropy of mixing in a specific series of theories of GPTs called the regular polygon theories, which can be regarded from a geometrical perspective as intermediate theories between a classical trit and a quantum bit with real coefficients. We prove that the operationally natural thermodynamical entropy of mixing does not exist in those inbetween theories, that is, the existence of the natural entropy results in classical and quantum-like theories among the regular polygon theories.

Interdependence and Superordinate Goals: The Revenge of the Dualists

Appearances can be misleading, but not in the social sciences. Based on the statistical aggregation of intuitions (observations, self-reports, interviews) about reality across individuals that converge while seeking a 1:1 relation, the primary model of decision making attempts to make intuitions rational. But despite its many claims to the contrary, the social sciences have failed in building a successful predictive theory, including in economics where the results from this failure, re-labeled as irrational, have won Nobel prizes, yet irrational humans in freely organized and competitive teams strangely manage to be extraordinarily innovative. In contrast to traditional social science, the most predictive theory in all of science is the quantum theory, each prediction confirmed by new discoveries leading to new predictions and further discoveries, but the dualist nature of the quantum theory makes it counterintuitive despite more than a century of intense, unflagging debate. By re-introducing dualism into social science with a quantum-like theory of social interdependence, we offer an opportunity to rehabilitate social science by successfully making predictions and new discoveries about human teams that account for the abysmal performance of interdisciplinary science teams; that generalizes to the newly arising problem of how to engineer hybrid teams (arbitrary combinations of autonomous humans, machines and robots); and that explains the counterintuitive prediction that highly interdependent teams do not generate Shannon information, but instead “darken” as a team becomes perfect, meaning, intuitively, that structural information about a team can be gained only under competition (i.e., perturbation theory).

Emergent "Quantum" Theory in Complex Adaptive Systems.

Motivated by the question of stability, in this letter we argue that an effective quantum-like theory can emerge in complex adaptive systems. In the concrete example of stochastic Lotka-Volterra dynamics, the relevant effective "Planck constant" associated with such emergent "quantum" theory has the dimensions of the square of the unit of time. Such an emergent quantum-like theory has inherently non-classical stability as well as coherent properties that are not, in principle, endangered by thermal fluctuations and therefore might be of crucial importance in complex adaptive systems.

Phase Groups and the Origin of Non-locality for Qubits

We describe a general framework in which we can precisely compare the structures of quantum-like theories which may initially be formulated in quite different mathematical terms. We then use this framework to compare two theories: quantum mechanics restricted to qubit stabiliser states and operations, and Spekkens's toy theory. We discover that viewed within our framework these theories are very similar, but differ in one key aspect – a four element group we term the phase group which emerges naturally within our framework. In the case of the stabiliser theory this group is Z4 while for Spekkens's toy theory the group is Z2×Z2. We further show that the structure of this group is intimately involved in a key physical difference between the theories: whether or not they can be modelled by a local hidden variable theory. This is done by establishing a connection between the phase group, and an abstract notion of GHZ state correlations. We go on to formulate precisely how the stabiliser theory and toy theory are ‘similar’ by defining a notion of ‘mutually unbiased qubit theory’, noting that all such theories have four element phase groups. Since Z4 and Z2×Z2 are the only such groups we conclude that the GHZ correlations in this type of theory can only take two forms, exactly those appearing in the stabiliser theory and in Spekkens's toy theory. The results point at a classification of local/non-local behaviours by finite Abelian groups, extending beyond qubits to finitary theories whose observables are all mutually unbiased.

PATH INTEGRAL APPROACH IN QUANTUM-LIKE THEORY.

A formulation of the Quantum-like theory based on Feynman's propagator is presented for particle beams. Applications to betatronic oscillations of LHC and HIDIF show encouranging predictions.

Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field.

We report here the observations that exhibit the existence of matter wave phenomena with wavelength in the macrodomain of a few centimeters, for electrons moving along a magnetic field from an electron gun to a collector plate situated behind a grounded grid. These are in accordance with the predictions of a quantumlike theory for charged particles in the classical macrodomain, given by one of the authors [R. K. Varma, Phys. Rev. A 31, 3951 (1985)] with a recent generalization [R. K. Varma, Phys. Rev. E 64, 036608 (2001)]. The beats correspond to two closely spaced "frequencies" in the system, with the beat frequency given, in accordance with the characteristics of a wave phenomena, by the difference between the two frequencies. The beats ride as a modulation over a discrete energy band structure obtained with only one frequency present. The frequency here corresponds to the distance between the electron gun and the detector plate as it characterizes the variation in the energy band structure as the electron energy is swept. The second "frequency" corresponds to the gun-grid distance. These observations of the beats of matter waves in this experiment, with characteristics in accordance with the wave algorithm, then establish unambiguously the existence of macroscopic matter waves for electrons propagating along a magnetic field.

Quantum approach to the halo formation in high current beams

An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined.

Noncommutative Tomography of an Analytic Signal and Entanglement in the Probability Representation of Quantum Mechanics

A review of new results in the quantumlike theory of an analytic signal (used in information processing) on the basis of the recently developed approach of the tomographic description of quantum states in quantum mechanics is presented. The procedure of noncommutative tomography of the analytic signal is used to study the analytic signal depending both on the spatial variable and the time. The entanglement theory of the analytic signal in the noncommutative‐tomography scheme is discussed in connection with information processing, and the possibility to use optical fibers for the simulation of quantum entanglement relevant to quantum computing is suggested.

Role of semiclassical description in the quantumlike theory of light rays.

An alternative procedure to the one by Gloge and Marcuse [J. Opt. Soc. Am. 59, 1629 (1969)] for performing the transition from geometrical optics to wave optics in the paraxial approximation is presented. This is done by employing a recent "deformation" method used to give a quantumlike phase-space description of charged-particle-beam transport in the semiclassical approximation. By taking into account the uncertainty relation (diffraction limit) that holds between the transverse-beam-spot size and the rms of the light-ray slopes, the classical phase-space equation for light rays is deformed into a von Neumann-like equation that governs the phase-space description of the beam transport in the semiclassical approximation. Here, Planck's constant and the time are replaced by the inverse of the wave number, not lambda, and the propagation coordinate, respectively. In this framework, the corresponding Wigner-like picture is given and the quantumlike corrections for an arbitrary refractive index are considered. In particular, it is shown that the paraxial-radiation-beam transport can also be described in terms of a fluid motion equation, where the pressure term is replaced by a quantumlike potential in the semiclassical approximation that accounts for the diffraction of the beam. Finally, a comparison of this fluid model with Madelung's fluid model is made, and the classical-like picture given by the tomographic approach to radiation beams is advanced as a future perspective.

Quantum-like approach to the transversal and longitudinal beam dynamics. The halo problem

An interpretation of the formation of halo in accelerators based on quantum-like theory by a diffraction model is given in terms of the transversal beam motion. Physical implications of the longitudinal dynamics are also examined.

EXPERIMENTAL TEST OF A QUANTUM-LIKE THEORY: MOTION OF ELECTRONS IN A UNIFORM MAGNETIC FIELD, IN A VARIABLE POTENTIAL WELL

We describe an experiment to test a quantum-like theory which predicts quantum-like behavior for an ensemble of electrons in a classical configuration with static magnetic and electric fields. Some of the earlier experiments had supporting evidence for anomalous, quantum-like effects in such a situation showing systematic modulations of electron current when a retarding potential is varied, even though the quantum wavelength of the electrons in such a configuration was less than a billionth of the spatial width of the potential well. Our experiment conclusively rules out any nonclassical, quantum-like behavior in electron transmission through simple electric barriers, when magnetic fields are present. We identify secondary electrons generated at various electrodes as the main source of apparent anomalous behavior. We also present a classical derivation of the quantum-like equation describing the modulations.

A quantum-like theory of wave propagation in periodic structures

Recent investigations of wave propagation in numerical computing domains in which hyperbolic equations are approximated with finite differences (typically in the context of computational fluid dynamics) have brought to the fore striking similarities between this class of phenomena and corresponding aspects of quantum mechanics: those have been reported in Refs [l, 2]. This has pointed toward the possibility of formulating a theory that would parallel Schr6dinger's theory of particle physics, and that would explain those similarities. Further investigation did show that this was indeed the case: it was shown in Ref. [3] that, as expected (but nevertheless surprisingly), such a new formalism may indeed be established. While these results were obtained in the context of numerical computing, nothing in their mathematics was of such a nature that their applicability should remain restricted to that specific case. That this is indeed true is demonstrated in the present paper by extending those previous results to the description of wave propagation in the periodic system consisting of a taut, massless string to which point masses are attached almost periodically (that is to be considered as a model of a broad class of physical periodic systems). Other aspects of this may be found in Refs [4, 5]. Part of the new results consist in showing that many of the known properties of classical wave propagation in periodic structures may be described by a formalism and by mathematics similar to those of the wave mechanics component of quantum mechanics. They also show that certain phenomena that were considered as strictly atomic scaled, such as tunneling, also occur in large scale periodic systems, such as the discretized string, with an identical theoretical explanation. As indicated, it is in the context of numerical computing that the phenomena which have suggested the new theory were first brought to light. We show (using the the string of point masses as an example) that the theory applies also to physical (as opposed to numerical) systems and it will apply as a matter of fact to the other periodic structures which are described by similar mathematics. That no such results have been reported so far in the relevant literature in physics may be attributed in part to the fact that some of the most vivid evidence of quantum-like phenomena may be observed in numerical computing, in experiments with nonuniform grids [6-8]: while nonuniform periodic structures are very common in numerical computing, their occurrence in physical systems is quite rare, and the analysis of wave propagation in classical periodic structures has been devoted almost exclusively to piecewise uniform systems [9, 10]. But this absence of precedents coming from physics may also be attributed to the simple fact that physical systems do not allow for experiments to be created and for the corresponding data to be measured with the same ease and accuracy as in numerical computing. There are of course many examples for this role of computing in the discovery and investigation of new mathematical concepts and physical phenomena: see for instance Zabusky [l 1] for an interesting account of the discovery of solitons, which followed the now famous Fermi-Pasta-Ulam (1955) computer experiments with the discrete space analog of a nonlinear vibrating string.