# Andrei KhrennikovLinnaeus University | lnu · Faculty of Technology

Andrei Khrennikov

PhD, ``kandidate'' of physics-mathematics, Moscow State University, 1983; Doctor of physics-mathematics, Steklov Mathematical Institute of Soviet Academy of Science, 1989

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## Publications

Publications (1,189)

Introduction to theory of social laser, Kyoto, November 2, 2023

Contents of th book
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Arkady Plotnitsky and Emmanuel Haven 1
On Wheeler’s Quantum Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gregg Jaeger 25
Letters for Andrei: QBism and the Unfinished Nat...

This is an introduction to quantum-like modeling of cognition, decision making, and artificial intelligence.

Over the last ten years, elements of the formalism of quantum mechanics have been successfully applied beyond physics in areas such as psychology (especially cognition), economics and finance (especially in the formalization of so-called ‘decision making’), political science, and molecular biology. An important stream of work along these lines, com...

Biological systems have been shown to have quantum-like behaviors by applying the adaptive dynamics view on their interaction networks. In particular, in the process of lactose–glucose metabolism, cells generate probabilistic interference patterns similarly to photons in the two-slit experiment. Such quantum-like interference patterns can be found...

Quantum mechanics (QM) is derived based on a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between events. Al...

Diversity of interpretations of quantum mechanics is often considered as a sign of foundational crisis. In this note we proceed towards unification the relational quantum mechanics of Rovelli, Bohmian mechanics, and many worlds interpretation on the basis so called Dendrogramic Holographic Theory (DHT). DHT is based on the representation of observe...

This paper is devoted to the event-observational modelling in physics and more generally natural science. The basic entities of such modelling are events and where space-time is the secondary structure for representation of events. The novelty of our approach is in using new mathematical picture for events universe. The events recorded by an observ...

This paper provides for a general overview of some of the main areas of applications where we believe the formalism from quantum mechanics has been (and can be) fruitfully applied. Over the past decade, progress has been made on using elements of this formalism in decision making models but also in data retrieval approaches and even in areas such a...

We present the mathematical model of cooperative functioning of unconscious and consciousness. The model is based on the theory of open quantum systems. Unconscious and consciousness are treated as bio-information systems. The latter plays the role a measurement apparatus for the former. States of both systems are represented in Hilbert spaces. Con...

This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables A and B, so this is AB-en...

We developed the novel mathematical model for event-universe by representing events as branches of dendrograms (finite trees) expressing the hierarchic relation between events. At the ontic level we operate with infinite trees. Algebraically such mathematical structures are represented as p-adic numbers. We call this kind of event mechanics Dendrog...

We start with a brief review on social laser theory which is newly framed with the notion of an infon–social energy quantum carrying coarse-grained information content. Infons are the excitations of the quantum social-information field. Humans are analogues of atoms—social atoms absorbing and emitting infons. Another new development is coupling of...

The combination of the question order and response replicability effects (QOE+RRE) cannot be modeled by von Neumann observables (with projection state update). In this chapter, we overcome this difficulty within quantum instrument theory. The mathematical construction is based on the indirect measurement scheme. The unitary operators describing the...

The unconscious-conscious framework is explored for quantum-like modeling of interconnected dynamics of perceptions and emotions. More generally this framework describes the emotional coloring process for the variety of conscious experiences, including decision-making. There are considered two classes of observables: perceptions and emotions. These...

Stability of social and behavioral order in biological, ecological, and social systems can be modeled with the aid of bio-social information analogue of the mathematical formalism describing the Fröhlich condensation. The latter is a high temperature analogue of the Bose–Einstein condensation and system’s stability is based on intensive pumping of...

In this chapter, we briefly present the expected utility theory developed by von Neumann and Morgenstern and subjective expected utility theory developed by Savage. The limits of their applications are illustrated by the Allais and Ellsberg paradoxes. These paradoxes are presented with contextual structuring corresponding to different gambles. The...

Wang and Busemeyer derived the famous QQ-equality (QQE), amazing (and unexpected) property of cognitive and social data. As a special psychological effect, QQE can be easily described by the standard von Neumann measurement theory, with Hermitian operators and the projection state update. However, von Neumann theory is not powerful enough to descri...

This part of the book is based on my article [297] written for the volume which should be published within the Templeton foundation project “Matter and Consciousness”. I was one of the external advisers for a group of Russian orthodox priests in St. Petersburg working within the project. Unfortunately, this project was broken as the result of the s...

Thermodynamics was created to describe statistical behavior of physical systems. However, its formalism can be applied to arbitrary systems such that it is possible to determine the states corresponding to the fixed values of some quantity, “energy” E. This quantity has to be additive with respect to the elements of the systems ensembles. Both phys...

This chapter presents the motivation for employing quantum probability (QP), instead of classical probability (CP), the mathematical modeling in cognitive psychology and decision-making. We refer to the Kahneman and Tversky works pointed out that CP using as the basis of decision theory leads to inconsistencies and paradoxes. Such motivation is not...

Starting with highlighting the Bohr complementarity principle, we analyze the notion of contextuality. The latter is understood as the irreducible dependence of observable’s outcome on the experimental context. Thus, the outcomes of quantum observables are generated in the complex process of system-apparatus interaction. Such Bohr-contextuality is...

This chapter presents the quantum-like model of information processing by brain’s neural networks. The model does not refer to the genuine quantum physical processes in the brain. Hence, it does not suffer of the well known problems of matching of the quantum and neural scales (temporal, spatial, temperature). In this model, uncertainty generated b...

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-modeling. In this chapter, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger stressed that order stability is one of the charact...

How far can one proceed with quantum formalism in modeling psychological effects? It is clear that each theory has its own domain of applicability. By borrowing the formalism of quantum mechanics (QM) and applying it in psychology, cognitive, social, and political sciences, one has to be aware that once he might approach the boundary of applicabili...

This chapter combines the ideas and methods of quantum theory and social engineering. Although it is rather eclectic, the reader may recognize usefulness of social laser theory for modeling of social processes and understanding techniques of modern social engineering. Everybody would agree that during the last years human society was permanently di...

We recount the fundamentals of the quantum-like modeling of decision-making. The basic scheme explores the standard quantum measurement theory. Questions, problems, and tasks are described by quantum observables, Hermitian operators, and belief or mental states of decision makers by quantum states, normalized vectors in a complex Hilbert space or g...

In this chapter, we start the journey to the complex world of quantum instruments. First, we reformulate the standard von Neumann measurement theory and exclude Hermitian operators from consideration. Instrument-representation of quantum measurement theory is the advanced part of quantum theory. The basic quantum observables as say position and mom...

This chapter is continuation of Chap. 4 attempting to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. We consider a complex biosystem S composed of many subsystems, say proteins, or cells, or neural networks in the brain, i.e., \(S=(S_i).\) We study the following problem: if the com...

This chapter presents the basics of the quantum formalism and axiomatics. The introduction is rather long, although elementary. (The readers who had some course in quantum physics can jump directly to further chapters.) Mathematically quantum theory is based on the linear algebra in complex Hilbert space coupled to probability theory. In two words,...

The Savage Sure thing principle is the starting point of the discussion on CP versus QP-based notions of rationality. The problem of rationality is coupled with the disjunction and question order effects. The attempt to combine the latter with another psychological effect, response replicability effect, make to question the possibility to use the s...

This chapter is not so difficult for reading, but a reader inexperienced in the foundational problems may be disappointed by the diversity of the opinions on the possible interpretations of a quantum state (wave function). One may skip this chapter and explore the quantum-like models of this book without setting some interpretation to mathematical...

The social laser is based on a well-known in quantum physics laser model of coherent amplification of the optical field. As was discussed in Chap. 11, social networks are at the core of the social laser model. In the present chapter, they are defined by means of a network model possessing power-law degree distribution. Decision-making agents (human...

Quantum-like modeling led to a number of foundational questions. Nowadays we can speak about a new science—foundations of quantum-like modeling. At the beginning the main attention was paid to comparison of classical and quantum probabilistic models. It was found that statistical data from cognitive psychology violate some basic constraints posed o...

The aim of this review is to highlight the possibility of applying the mathematical formalism and methodology of quantum theory to model behavior of complex biosystems, from genomes and proteins to animals, humans, and ecological and social systems. Such models are known as quantum-like, and they should be distinguished from genuine quantum physica...

This is a brief review on the basics of recently established Dendrogramic Holographic theory (DH-theory). This is the special model of the event-universe based on the clustering transformation of experimental data into dendrogram, a finite tree which branches encoding the events. These event-branches are coupled via the hierarchic interrelation det...

The aim of this review is to highlight the possibility to apply the mathematical formalism and methodology of quantum theory to model behaviour of complex biosystems, from genomes and proteins to animals, humans, ecological and social systems. Such models are known as quantum-like and they should be distinguished from genuine quantum physical model...

This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable A and B. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables A and B, so this is AB-en...

We developed the novel mathematical model for event-universe by representing events as branches of dendrograms (finite trees) expressing the hierarchic relation between evens. At the ontic level we operate with infinite trees. Algebraically such mathematical structures are represented as p-adic numbers. We call this kind of event mechanics Dendrogr...

The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and disjunction. It is well known that nondistributivity is equivalent to incompatibility of logical variables — the impos...

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 i...

Closed timelike curves (CTCs) are non-intuitive theoretical solutions of general relativity field equations. The main paradox associated with the physical existence of CTCs, the so-called grandfather paradox, can be satisfactorily solved by a quantum model named Deutsch-CTC. An outstanding theoretical result that has been demonstrated in the Deutsc...

The diagnosis of psychiatric disorders is currently based on a clinical and psychiatric examination (intake). Ancillary tests are used minimally or only to exclude other disorders. Here, we demonstrate a novel mathematical approach based on the field of p-adic numbers and using electroencephalograms (EEGs) to identify and differentiate patients wit...

QBism's foundational statement that ``the outcome of a measurement of an observable is personal'' is in the straight contraversion with Ozawa's Intersubjectivity Theorem (OIT). The latter (proven within the quantum formalism) states that two observers, agents within the QBism terminology, performing joint measurements of the same observable $A$ on...

Quantum mechanics (QM) is derived on the basis of a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between eve...

This note is devoted to the problem of signaling (marginal inconsistency) in the Bell-type experiments with physical and cognitive systems. It seems that in quantum physics, this problem is still not taken seriously. Only recently have experimenters started to check the signaling hypothesis for their data. For cognitive systems, signaling was stati...

This is a review on social laser theory completed with its new developments and applications. An important methodological step towards similarity with quantum physics is the invention and consistent operation with infons. These are excitations of the quantum social-information field carrying social energy and coarse grained content of communication...

This is a short version of the article
Basieva, I., and Khrennikov, A. (2022). Conditional probability framework for entanglement and its decoupling from tensor product structure. arXiv:2205.11510; 2022 J. Phys. A: Math. Theor. 55, 395302.

This is the brief review on quantum-like modeling, quantum probability versus classical probability in cognition, psychology, decision making, and artificial intelligence. We describe the problems induced by using classical probability (CP) for mathematical formalization of decision making—paradoxes and probability fallacies. These problems are rel...

This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, com...

The aim of this paper is to promote quantum logic as one of the basic tools for analyzing human reasoning. We compare it with classical (Boolean) logic and highlight the role of violation of the distributive law for conjunction and disjunction. It is well known that nondistributivity is equivalent to incompatibility of logical variables -- the impo...

Our aim is to make a step towards clariﬁcation of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schrödinger’s words, this is entanglement of knowledge which can be extracted via conditional measurements. In particular, quantum probabilities are interpreted...

This is a review devoted to the complementarity-contextuality interplay with connection to the Bell inequalities. Starting discussion with complementarity, we point out to contextuality as its seed. {\it Bohr-contextuality} is dependence of observable's outcome on the experimental context, on system-apparatus interaction. Probabilistically, complem...

Quantum mechanics (QM) is derived based on a universe composed solely of events, for example, outcomes of observables. Such an event universe is represented by a dendrogram (a finite tree) and in the limit of infinitely many events by the p-adic tree. The trees are endowed with an ultrametric expressing hierarchical relationships between events. Al...

This is the short version of my resent studies on social Fröhlich condensation and it role in establishing societal stability.

This a review of on quantum-like modeling of cognition, decision making, and social processes

Applications of the mathematical apparatus of quantum theory to decision making, economics, and finances should be accommodated with the foundations of this theory. Quantum nonlocality (spooky action at a distance) is one of the most exiting features of modern quantum theory. This is one of the main challenges in justification of applications of th...

Recently we started the development of Dendrographic Hologram Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of Smolin et al.). Elementary events are represented by branches of dendrograms, finite trees that are generated from data with clustering algorithms. In this context,...

Our aim is to make a step towards clarification of foundations for the notion of entanglement (both physical and mathematical) by representing it in the conditional probability framework. In Schr\"odinger's words, this is entanglement of knowledge which can be extracted via conditional measurements. In particular, quantum probabilities are interpre...

In this work we suggest a novel paradigm of social laser (solaser), which can explain such Internet inspired social phenomena as echo chambers, reinforcement and growth of information cascades, enhancement of social actions under strong mass media operation. The solaser is based on a well-known in quantum physics laser model of coherent amplificati...

An intuition of ambivalence in cognition is particularly strong for complex decisions, for which the merits and demerits of different options are roughly equal but hard to compare. We examined information search in an experimental paradigm which tasked participants with an ambivalent question, while monitoring attentional dynamics concerning the in...

These are very simple (may be even primitive) notes on quantum-like modeling, practically without mathematical formulas.

Recently we started the development of Holographic Dendrogramic Theory (DH-theory). It is based on the novel mathematical representation of the relational event universe (in the spirit of (Smolin, Barbour, Rovelli). Elementary events are represented by branches of dendrograms, finite trees, which are generated from data with clustering algorithms....

This is a short introductory review on application of quantum probability (QP) in physics, cognitive studies, artificial intelligence, psychology, decision making, social and political sciences. We emphasize that QP is a contextual probability theory that is based on the quantum-like contextual paradigm: QP formalism can be used to model behavior n...

Purpose
This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modeling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature.
Design/methodo...

Nowadays, contextuality is the hottest topic of quantum foundations and, especially, foundations of quantum information theory. This notion is characterized by the huge diversity of approaches and interpretations. One of the strongest trends in contextual research is to identify contextuality with Bell test contextuality (BTC). In this paper, we cr...

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is b...

Closed timelike curves (CTCs), non-intuitive theoretical solutions of general relativity field equations can be modelled in quantum mechanics in a way, known as Deutsch-CTCs, to circumvent one of their most paradoxical implications, namely, the so-called grandfather paradox. An outstanding theoretical result of this model is the demonstration that...

This is a short introductory review on quantum-like modeling of cognition with applications to decision-making and rationality. The aim of the review is twofold: (a) to present briefly the apparatus of quantum information and probability theory useful for such modeling; (b) to motivate applications of this apparatus in cognitive studies and artific...

This paper is a part of the volume devoted to Templeton foundation project "Matter and Consciousness". We present briefly Bohr's views and the Copenhagen interpretation of quantum mechanics, with emphasizing the role of contextuality, complementarity, and free will. Then we turn to Quantum Bayesianism (QBism) as one of the quantum foundational flow...

Nowadays contextuality is the hotest topic of quantum foundations and, especially, foundations of quantum information theory. This notion is characterized by the huge diversity of approaches and interpretations. One of the strongest trends in contextual research is to identify contextuality with violation of the Bell inequalities. We call this sort...

Purpose: This paper aims to present the basic assumptions for creation of social Frohlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature. Design method...

Stability of social and behavioural order in biological, ecological, and social systems is modelled within the formalism of the Fröhlich condensation. The latter is a high temperature analogue of the Bose-Einstein condensation and stability is approached via intensive pumping of energy into a system interacting with a bath. We start with the review...

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is b...

Purpose – This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature.
Design/metho...

This paper aims to present the basic assumptions for creation of social Fröhlich condensate and attract attention of other researchers (both from physics and socio-political science) to the problem of modelling of stability and order preservation in highly energetic society coupled with social energy bath of high temperature. The model of social Fr...

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman’s conclusion on the impossibility to apply the classical probabilistic description for the two slit e...

No diagnostic or predictive instruments to help with early diagnosis and timely therapeutic intervention are available as yet for most neuro-psychiatric disorders. A quantum potential mean and variability score (qpmvs), to identify neuropsychiatric and neurocognitive disorders with high accuracy, based on routine EEG recordings, was developed. Info...

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; i...

We present a new mathematical model of disease spread reflecting some specialties of the covid-19 epidemic by elevating the role of hierarchic social clustering of population. The model can be used to explain slower approaching herd immunity, e.g., in Sweden, than it was predicted by a variety of other mathematical models and was expected by epidem...

In quantum physics, the notion of contextuality has a variety of interpretations, which are typically associated with the names of their inventors, say, Bohr, Bell, Kochen, Specker, and recently Dzhafarov. In fact, Bohr was the first who pointed to contextuality of quantum measurements as a part of formulation of his principle of complementarity. (...

Quantum measurement theory is applied to quantum-like modeling of coherent generation of perceptions and emotions and generally for emotional coloring of conscious experiences. In quantum theory, a system should be separated from an observer. The brain performs self-measurements. To model them, we split the brain into two subsystems, unconsciousnes...

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit e...

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit e...

Recently quantum probability theory started to be actively used in studies of human decision-making, in particular for the resolution of paradoxes (such as the Allais, Ellsberg, and Machina paradoxes). Previous studies were based on a cognitive metaphor of the quantum double-slit experiment—the basic quantum interference experiment. In this paper,...

We present a new mathematical model of disease spread reflecting some specialities of the covid-19 epidemic by elevating the role of hierarchic social clustering of population. The model can be used to explain slower approaching herd immunity, e.g., in Sweden, than it was predicted by a variety of other mathematical models and was expected by epide...

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH-theory). We use the ontic-epistemic (implicate-explicate order) methodology. The epistemic counterpart is based on representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic Universe is described as the p-adic tree; it i...

In spite of numerous predictions, the natural herd immunity for covid-19 visru had not been approahed anywhere in the world. Thus, the traditional mathematical models of disease spread demonstrated their inability to describe adequately the covid-19 pandemic. In au-thor's works, the novel model of the disease spread was developed. This model reflec...

Ultrametric model of disease spread taking into account specialities of COVID-19 epidemic

In spite of numerous predictions, the natural herd immunity for covid-19 visru had not been approahed anywhere in the world. Thus, the traditional mathematical models of disease spread demonstrated their inability to describe adequately the covid-19 pandemic. In author's works, the novel model of the disease spread was developed. This model reflect...

Quantum measurement theory is applied to quantum-like modeling of coherent generation of perceptions and emotions and generally for emotional coloring of conscious experiences. In quantum theory, a system should be separated from an observer. The brain performs self-measurements. To model them, we split the brain into two subsystems, unconsciousnes...

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of...

A proposal for a fundamental theory is described in which classical and quantum physics as a representation of the universe as a gigantic dendrogram are unified. The latter is the explicate order structure corresponding to the purely number-theoretical implicate order structure given by p-adic numbers. This number field was zero-dimensional, totall...

The recent claim of Google to have brought forth a breakthrough in quantum computing represents a major impetus to further analyze the foundations for any claims of superiority regarding quantum algorithms. This note attempts to present a conceptual step in this direction. I start with a critical analysis of what is commonly referred to as entangle...

We present the mathematical model of cooperative functioning of unconscious and consciousness. The model is based on the theory of open quantum systems. Unconscious and consciousness are treated as bio-information systems. The latter plays the role a measurement apparatus for the former. States of both systems are represented in Hilbert spaces. Con...

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent...