Quantum-like Research Articles

Quantum-like states on complex synchronized networks

Recent work has exposed the idea that interesting quantum-like (QL) probability laws, including interference effects, can be manifest in classical systems. Here, we propose a model for QL states and QL bits. We suggest a way that huge, complex systems can host robust states that can process information in a QL fashion. Axioms that such states should satisfy are proposed. Specifically, it is shown that building blocks suited for QL states are networks, possibly very complex, that we defined based on k -regular random graphs. These networks can dynamically encode a lot of information that is distilled into the emergent states we can use for QL processing. Although the emergent states are classical, they have properties analogous to quantum states. Concrete examples of how QL functions are possible are given. The possibility of a ‘QL advantage’ for computing-type operations and the potential relevance for new kinds of function in the brain are discussed and left as open questions.

'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)'.

"Most tantumising state of affairs": Mathematical and non-mathematical in quantum-like understanding of thinking.

This article addresses the effectiveness of the predictive modeling of cognition and behavior based on quantum principles and some of the reasons for this effectiveness. It also aims, however, to explore the limitations of mathematical modeling so based, quantum-like (Q-L) modeling, and all mathematical modeling, including classical-like (C-L), in considering human cognition and behavior. It will discuss certain alternative approaches to both, essentially philosophical in nature, although sometimes found in literary works, approaches that, while not quantitative, may help compensate for limitations of mathematical modeling there. Most Q-L and C-L approaches beyond physics are realist, insofar as they offer representations of human thinking by the formalism of quantum or classical physical theories. The position adopted in this article is based on the non-realist assumption that such a representation may not be possible, which is not the same as that it is impossible. I designate interpretations that do not make this assumption reality-without-realism, RWR, interpretations, and in considering mental processes as ideality-without-idealism, IWI, interpretations.

Complementarity of Mental Observables

AbstractThe 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.

Comment on Masanari Asano et al.: A model of epigenetic evolution based on theory of open quantum systems.

In a recent publication, ‘A model of epigenetic evolution based on theory of open quantum systems’ (2013), the authors state: “We call our model quantum-like (QL) to distinguish it from really quantum models in cell biology: reducing cell’s behavior to quantum particles inside a cell, e.g., (Ogryzko 2008, 1997), McFadden and Al-Khalili (McFadden and Al-Khalili 1999), McFadden (McFadden 2000).”

Quantum-like model of diauxie in Escherichia coli: Operational description of precultivation effect

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 coli. 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 bio-chemical 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.

Quantum-like model of processing of information in the brain based on classical electromagnetic field

Abstract We propose a model of quantum-like (QL) processing of mental information. This model is based on quantum information theory. However, in contrast to models of “quantum physical brain” reducing mental activity (at least at the highest level) to quantum physical phenomena in the brain, our model matches well with the basic neuronal paradigm of the cognitive science. QL information processing is based (surprisingly) on classical electromagnetic signals induced by joint activity of neurons. This novel approach to quantum information is based on representation of quantum mechanics as a version of classical signal theory which was recently elaborated by the author. The brain uses the QL representation (QLR) for working with abstract concepts; concrete images are described by classical information theory. Two processes, classical and QL, are performed parallely. Moreover, information is actively transmitted from one representation to another. A QL concept given in our model by a density operator can generate a variety of concrete images given by temporal realizations of the corresponding (Gaussian) random signal. This signal has the covariance operator coinciding with the density operator encoding the abstract concept under consideration. The presence of various temporal scales in the brain plays the crucial role in creation of QLR in the brain. Moreover, in our model electromagnetic noise produced by neurons is a source of superstrong QL correlations between processes in different spatial domains in the brain; the binding problem is solved on the QL level, but with the aid of the classical background fluctuations.

On the Physical Basis of Theory of “Mental Waves”

We discuss the conjecture on quantum-like (QL) processing of information in the brain. It is not based on the physical quantum brain (e.g., Penrose) - quantum physical carriers of information. In our approach the brain created the QL representation (QLR) of information in Hilbert space. It uses quantum information rules in decision making. The existence of such QLR was (at least preliminary) confirmed by experimental data from cognitive psychology; in particular, experiments on recognition of ambiguous figures (Conte et al., 2006; 2009). The violation of the law of total probability in these experiments is an important sign of nonclassicality of data. In this paper we speculate on a possible physical realization of QLR in the brain: a classical wave model producing QLR . It is based on variety of time scales in the brain. Each pair of scales (fine - the background fluctuations of electromagnetic field and rough - the cognitive image scale) induces the QL representation. The background field plays the crucial role in creation of “superstrong QL correlations” in the brain.

Quantum-like model of cognitive decision making and information processing

In this paper we offer the quantum-like (QL) representation of the Shafir–Tversky statistical effect which is well known in cognitive psychology. We apply the so-called contextual approach. We consider the Shafir–Tversky effect to result from mixing statistical data obtained in incompatible contexts which are involved, e.g. in Prisoner’s Dilemma or in more general games in which the disjunction effect can be found. As a consequence, the law of total probability is violated for the experimental data obtained in experiments on cognitive psychology by Shafir and Tversky [Shafir, E., Tversky, A., 1992. Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474] as well as Tversky and Shafir [Tversky, A., Shafir, E., 1992. The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309]. Moreover, we can find a numerical measure of contextual incompatibility (the so-called coefficient of interference) as well as represent contexts which are involved in Prisoner’s Dilemma (PD) by probability amplitudes—normalized vectors (“mental wave functions”). We remark that statistical data from Shafir and Tversky [Shafir, E., Tversky, A., 1992. Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474] and Tversky and Shafir [Tversky, A., Shafir, E., 1992. The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309] experiments differ crucially from the point of view of mental interference. The second one exhibits the conventional trigonometric ( cos ⁡ -type) interference while the first one exhibits even the so-called hyperbolic ( cosh ⁡ -type) interference. We discuss the QL processing of information by cognitive systems, especially, the QL decision making and both classical and QL rationality and ethics.

Algorithm for Quantum-like Representation: Transformation of Probabilistic Data into Vectors on Bloch's Sphere

In this paper, we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed, cf. [1] and [2] on recent numerical simulation for quantum correlations. The Bloch's sphere is used for the visualization of results of numerical simulation. On the one hand, creation of such a quantum-like (QL) representation and its numerical approval is an important step in clarification of extremely complicated interrelation between classical and quantum randomness. On the other hand, it opens new possibilities for applying the mathematical formalism of QM in other domains of science.

Quantum-like microeconomics: Statistical model of distribution of investments and production

In this paper we demonstrate that the probabilistic quantum-like (QL) behavior–the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators, Schrödinger’s dynamics–can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems (commodities) are macroscopic. They could not be superpositions of two different states. In our approach the QL-behavior of economical statistics is a consequence of the organization of the process of production as well as investments. In particular, Hamiltonian (“financial energy”) is determined by rate of return.

Can Quantum Information be Processed by Macroscopic Systems?

We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the mathematical quantum formalism to probabilities induced in any domain of science. In our model quantum randomness appears not as irreducible randomness (as it is commonly accepted in conventional quantum mechanics, e.g., by von Neumann and Dirac), but as a consequence of obtaining incomplete information about a system. We pay main attention to the QL description of processing of incomplete information. Our QL model can be useful in cognitive, social and political sciences as well as economics and artificial intelligence. In this paper we consider in a more detail one special application---QL modeling of brain's functioning. The brain is modeled as a QL-computer.

Quantumlike representation of extensive form games: Probabilistic aspects

We consider an application of the mathematical formalism of quantum mechanics outside physics, namely, to game theory. We present a simple game between macroscopic players, say, Alice and Bob (or in a more complex form—Alice, Bob, and Cecilia), which can be represented in the quantumlike (QL) way—by using a complex probability amplitude (game’s “wave function”) and noncommutative operators. The crucial point is that games under consideration are so-called extensive form games. Here the order of actions of players is important; such a game can be represented by the tree of actions. The QL probabilistic behavior of players is a consequence of incomplete information (which is available to, e.g., Bob) about the previous action of Alice. In general one could not construct a classical probability space underlying a QL game. This can happen even in a QL game with two players. In a QL game with three players Bell’s inequality can be violated. The most natural probabilistic description is given by the so-called contextual probability theory completed by the frequency definition of probability.

Quantum-like brain: “Interference of minds”

We present a contextualist statistical realistic model for quantum-like representations in physics, cognitive science, and psychology. We apply this model to describe cognitive experiments to check quantum-like structures of mental processes. The crucial role is played by interference of probabilities for mental observables. Recently one such experiment based on recognition of images was performed. This experiment confirmed our prediction on the quantum-like behavior of mind. In our approach “quantumness of mind” has no direct relation to the fact that the brain (as any physical body) is composed of quantum particles. We invented a new terminology “quantum-like (QL) mind.” Cognitive QL-behavior is characterized by a nonzero coefficient of interference λ . This coefficient can be found on the basis of statistical data. There are predicted not only cos ⁡ θ -interference of probabilities, but also hyperbolic cosh ⁡ θ -interference. This interference was never observed for physical systems, but we could not exclude this possibility for cognitive systems. We propose a model of brain functioning as a QL-computer (there is a discussion on the difference between quantum and QL computers).