arXiv subjects

Andrei Khrennikov

Publications and source records attributed to Andrei Khrennikov.

At least 37 records · Page 2Linked to original sources

arXiv2023

Unification of the MWI formalism and Bohmian mechanics for the ensembles of event universes in Minkowski-like space

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 observed events by dendrograms (finite trees) presenting observers subjective image of universe. Dendrograms encode the relational hierarchy between events, in applications they are generated by clustering algorithms; an algorithm with the branching index p >1 generate p-adic trees. The infinite p-adic tree represents the ontic event universe. We consider an ensemble of observers performing observations on each other and representing them by p-adic trees. In such observers universe we introduce a kind of Minkowski space structure, which is statistical by its nature. This model unites the observer/system discrepancy. Measurements are performed by observers on observers. Such observers universe is dynamically changing and is background independent since the space itself is emergent. And within this model, we unify the aforementioned interpretations.

quant-ph↗

arXiv2023

Open systems, quantum probability and logic for quantum-like modeling in biology, cognition, and decision making

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 modeling of biological phenomena. One of the distinguishing features of quantum-like models is their applicability to macroscopic biosystems, or to be more precise, to information processing in them. Quantum-like modeling has the base in quantum information theory and it can be considered as one of the fruits of the quantum information revolution. Since any isolated biosystem is dead, modeling of biological as well as mental processes should be based on theory of open systems in its most general form -- theory of open quantum systems. In this review we advertise its applications to biology and cognition, especially theory of quantum instruments and quantum master equation. We mention the possible interpretations of the basic entities of quantum-like models with special interest to QBism is as may be the most useful interpretation.

quant-ph↗

arXiv2023

Quantum-like modeling of the order effect in decision making: POVM viewpoint on the Wang-Busemeyer QQ-equality

In recent years, quantum mechanics has been actively used in areas outside of physics, such as psychology, sociology, theory of decision-making, game theory, and others. In particular, quantum mechanics is used to explain the paradoxes arising in cognitive psychology and decision making. Wang and Busemeyer invented a quantum model and approach as well as non-parametric equality (so-called QQ-equality), explaining the questions order effect. The primary objective of this note is to test the possibility to expand the Wang-Busemeyer model by considering questions which are mathematically represented by positive operator valued measures. We found that, for such observables, the QQ-equality can be violated. But, we also showed that, in principle, it is possible to reduce expanded model to the original Wang-Busemeyer model by expanding the context of the questions. This version of preprint is aimed to point out to annoying miscalculation in version 1. This miscalculation might mislead a reader who is not experienced in operating with POVMs. Otherwise the main line of construction and reasoning presented in version 1 is right and it can be easily completed by the reader on the basis of version 1 and the correction remark in version 2.

quant-ph↗

arXiv2023

Entanglement of observables: Quantum conditional probability approach

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-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization of the AB-entangled states as amplitude non-factorisable states. In the tensor product case, $AB$-entanglement implies standard entanglement, but not vice verse. AB-entanglement for dichotomous observables is equivalent to their correlation. We describe the class of quantum states that are A_u B_u-entangled for a family of unitary operators (u). Finally, observables entanglement is compared with dependence of random variables in classical probability theory.

quant-ph↗

arXiv2023

Emergent quantum mechanics of the event-universe, quantization of events via Denrographic Hologram Theory

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. All events are coupled through the tree structure. Such a holistic picture of event-processes was formalized within the Dendrographic Hologram Theory (DHT). The present paper is devoted to the emergence of QM from DHT. We used the generalization of the QM-emergence scheme developed by Smolin. Following this scheme, we did not quantize events but rather the differences between them and through analytic derivation arrived at Bohmian mechanics. Previously, we were able to embed the basic elements of general relativity (GR) into DHT, and now after Smolin-like quantization of DHT, we can take a step toward quantization of GR. Finally, we remark that DHT is nonlocal in the treelike geometry, but this nonlocality refers to relational nonlocality in the space of events and not Einstein's spatial nonlocality.

quant-ph↗

arXiv2023

Ozawa's Intersubjectivity Theorem as objection to QBism individual agent perspective

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 a system $S$ in the state $ψ$ should get the same outcome $A=x.$ In Ozawa's terminology, this outcome is intersubjective and it can't be treated as personal. This is the strong objection to QBism which can't survive without updating its principles. The essential aspect in understanding of the OIT-impact on QBism's foundations takes the notion of quantum observable. This paper comprises the complementary discussion highlighting the difference between the accurate, von Neumann, and inaccurate, noisy, quantum observables which are represented by PVMs and POVMs respectively. Moreover, we discuss the OIT-impact on the Copenhagen interpretation of quantum mechanics.

quant-ph↗

arXiv2022

Nondistributivity of human logic and violation of response replicability effect in cognitive psychology

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 impossibility to assign jointly the two-valued truth values to these variables. A natural question arises as to whether quantum logical nondistributivity in human logic can be tested experimentally. We show that testing the response replicability effect (RRE) in cognitive psychology is equivalent to testing nondistributivity -- under the prevailing conjecture that the mental state update generated by observation is described as orthogonal projection of the mental state vector (the projective update conjecture of Wang and Busemeyer). A simple test of RRE is suggested. In contrast to the previous works in quantum-like modeling, we proceed in the state-dependent framework; in particular, distributivity, compatibility, and RRE are considered in a fixed mental state. In this framework, we improve the previous result on the impossibility to combine question order and response replicability effects by using (von Neumann-Lüders) projective measurements.

q-bio.NC↗

arXiv2022

Contextuality, Complementarity, Signaling, and Bell tests

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, complementarity means that the {\it joint probability distribution} (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality and, hence, incompatibility. For context dependent probabilities, these inequalities may be violated. We stress that contextuality tested by the Bell inequalities is so called {\it joint measurement contextualit}y (JMC), the special case of Bohr's contextuality. Then, we examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often experimental data has signaling patterns. We discuss possible sources of signaling; for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of "pure contextualize" from data shadowed by signaling. This theory known as {\it Contextuality by Default} (CbD). It leads to inequalities with the additional term quantifying signaling, Bell-Dzhafarov-Kujala inequalities.

quant-ph↗

arXiv2022

Conditional probability framework for entanglement and its decoupling from tensor product structure

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 as conditional ones (as, e.g., by Ballentine). We restrict considerations to perfect conditional correlations (PCC) induced by measurements ("EPR entanglement"). Such entanglement is coupled to the pairs of observables with the projection type state update as the back action of measurement. In this way, we determine a special class of entangled states. One of our aims is to decouple the notion of entanglement from the compound systems. The rigid association of entanglement with the state of a few body systems stimulated its linking with quantum nonlocality ("spooky action at a distance"). However, already by Schrödinger entanglement was presented as knotting of knowledge (about statistics) for one observable A with knowledge about another observable B.

quant-ph↗

arXiv2021

Against identification of contextuality with violation of the Bell inequalities: lessons from theory of randomness

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 of contextuality {\it Bell test contextuality} (BTC). In this note, we criticize the BTC-approach. It can be compared with an attempt to identify the complex and theoretically nontrivial notion of randomness with a test for randomness (or a batch of tests, as the NIST-test). We advertize {\it Bohr contextuality} -- taking into account all experimental conditions (context). In the simplest case, the measurement context of an observable $A$ is reduced to joint measurement with a compatible observable $B.$ The latter definition was originally considered by Bell in relation to his inequality. We call it {\it joint measurement contextuality} (JMC). Although JMC is based on the use of counterfactuals, by considering it in the general Bohr's framework it is possible to handle JMC on physical grounds. We suggest (similarly to randomness) to certify JMC in experimental data with Bell tests, but only certify and not reduce.

quant-ph↗

arXiv2021

Social Fröhlich condensation: Preserving societal order through sufficiently intensive information pumping

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 methodology approach: The model of social Frohlich condensation and its analysis are based on the mathematical formalism of quantum thermodynamics and field theory (applied outside of physics). Findings: The presented quantum-like model provides the consistent operational model of such complex socio-political phenomenon as Frohlich condensation. Research limitations implications: The model of social Frohlich condensation is heavily based on theory of open quantum systems. Its consistent elaboration needs additional efforts. Practical implications: Evidence of such phenomenon as social Frohlich condensation is demonstrated by stability of modern informationally open societies. Social implications: Approaching the state of Frohlich condensation is the powerful source of social stability. Understanding its informational structure and origin may help to stabilize the modern society. Originality value: Application of the quantum-like model of Frohlich condensation in social and political sciences is really the novel and original approach to mathematical modeling of social stability in society exposed to powerful information radiation from mass-media and internet based sources.

physics.soc-ph↗

arXiv2021

Quantum-like model for unconscious-conscious interaction and emotional coloring of perceptions and other conscious experiences

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, unconsciousness and consciousness. They correspond to a system and an observer. The states of perceptions and emotions are described through the tensor product decomposition of the unconscious state space; similarly, there are two classes of observables, for conscious experiencing of perceptions and emotions, respectively. Emotional coloring is coupled to quantum contextuality: emotional observables determine contexts. Such contextualization reduces degeneration of unconscious states. The quantum-like approach should be distinguished from consideration of the genuine quantum physical processes in the brain (cf. Penrose and Hameroff). In our approach the brain is a macroscopic system which information processing can be described by the formalism of quantum theory.

q-bio.NC↗

arXiv2021

Formalization of Bohr's contextuality within theory of open quantum systems

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 and 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. (Instead of "contextuality", he considered dependence on "experimental conditions.") Unfortunately, the contextuality counterpart of the complementarity principle was overshadowed by the issue of incompatibility of observables. And the interest for contextuality of quantum measurements rose again only in connection with the Bell inequality. The original Bohr's contextuality, as contextuality of each quantum measurement, was practically forgotten. It was highlighted in the works of the author of this paper, with applications both to physics and cognition. In this note, the theory of open quantum systems is applied to formalization of Bohr's contextuality within the the scheme of indirect measurements. This scheme is widely used in quantum information theory and it leads to the theory of quantum instruments (Davis-Lewis-Ozawa). In this scheme, Bohr's viewpoint on contextuality of quantum measurements is represented in the formal mathematical framework.

quant-ph↗

arXiv2020

Contextuality versus Incompatibility

Our aim is to compare the fundamental notions of quantum physics - contextuality vs. incompatibility. One has to distinguish two different notions of contextuality, {\it Bohr-contextuality} and {\it Bell-contextuality}. The latter is defined operationally via violation of noncontextuality (Bell type) inequalities. This sort of contextuality will be compared with incompatibility. It is easy to show that, for quantum observables, there is {\it no contextuality without incompatibility.} The natural question arises: What is contextuality without incompatibility? (What is "dry-residue"?) Generally this is the very complex question. We concentrated on contextuality for four quantum observables. We shown that in the CHSH-scenarios (for "natural quantum observables") {\it contextuality is reduced to incompatibility.} However, generally contextuality without incompatibility may have some physical content. We found a mathematical constraint extracting the contextuality component from incompatibility. However, the physical meaning of this constraint is not clear. In appendix 1, we briefly discuss another sort of contextuality based on the Bohr's complementarity principle which is treated as the {\it contextuality-incompatibility principle}. Bohr-contextuality plays the crucial role in quantum foundations. Incompatibility is, in fact, a consequence of Bohr-contextuality. Finally, we remark that outside of physics, e.g., in cognitive psychology and decision making Bell-contextuality cleaned of incompatibility can play the important role.

quant-ph↗

arXiv2020

Modeling combination of question order effect, response replicability effect, and QQ-equality with quantum instruments

We continue to analyze basic constraints on the human decision making from the viewpoint of quantum measurement theory (QMT). As it has been found, the conventional QMT based on the projection postulate cannot account for the combination of the question order effect (QOE) and the response replicability effect (RRE). This was alarming finding for quantum-like modeling of decision making. Recently, it was shown that this difficulty can be resolved by using of the general QMT based on quantum instruments. In the present paper we analyse the problem of the combination of QOE, RRE, and the well-known QQ-equality (QQE). This equality was derived by Busemeyer and Wang and it was shown (in a joint paper with Solloway and Shiffrin) that statistical data from many social opinion polls satisfy it. Here we construct quantum instruments satisfying QOE, RRE and QQE. The general features of our approach are formalized with postulates that generalize (the Wang-Busemeyer) postulates for quantum-like modeling of decision making. Moreover, we show that our model closely reproduces the statistics of the well-known Clinton-Gore Poll data with a prior belief state independent of the question order. This model successfully corrects for the order effect in the data to determine the "genuine" distribution of the opinions in the Poll. The paper also provides an accessible introduction to the theory of quantum instruments - the most general mathematical framework for quantum measurements.

q-bio.NC↗

arXiv2020

Quantum-like modeling in biology with open quantum systems and instruments

We present the novel approach to mathematical modeling of information processes in biosystems. It explores the mathematical formalism and methodology of quantum theory, especially quantum measurement theory. This approach is known as {\it quantum-like} and it should be distinguished from study of genuine quantum physical processes in biosystems (quantum biophysics, quantum cognition). It is based on quantum information representation of biosystem's state and modeling its dynamics in the framework of theory of open quantum systems. This paper starts with the non-physicist friendly presentation of quantum measurement theory, from the original von Neumann formulation to modern theory of quantum instruments. Then, latter is applied to model combinations of cognitive effects and gene regulation of glucose/lactose metabolism in Escherichia coli bacterium. The most general construction of quantum instruments is based on the scheme of indirect measurement, in that measurement apparatus plays the role of the environment for a biosystem. The biological essence of this scheme is illustrated by quantum formalization of Helmholtz sensation-perception theory. Then we move to open systems dynamics and consider quantum master equation, with concentrating on quantum Markov processes. In this framework, we model functioning of biological functions such as psychological functions and epigenetic mutation.

physics.bio-ph↗

arXiv2020

Introductory review to quantum information retrieval

Recently people started to understand that applications of the mathematical formalism of quantum theory are not reduced to physics. Nowadays, this formalism is widely used outside of quantum physics, in particular, in cognition, psychology, decision making, information processing, especially information retrieval. The latter is very promising. The aim of this brief introductory review is to stimulate research in this exciting area of information science. This paper is not aimed to present a complete review on the state of art in quantum information retrieval.

cs.IR↗

arXiv2020

True Contextuality Beats Direct Influences in Human Decision Making

In quantum physics there are well-known situations when measurements of the same property in different contexts (under different conditions) have the same probability distribution, but cannot be represented by one and the same random variable. Such systems of random variables are called contextual. More generally, true contextuality is observed when different contexts force measurements of the same property (in psychology, responses to the same question) to be more dissimilar random variables than warranted by the difference of their distributions. The difference in distributions is itself a form of context-dependence, but of another nature: it is attributable to direct causal influences exerted by contexts upon the random variables. The Contextuality-by-Default (CbD) theory allows one to separate true contextuality from direct influences in the overall context-dependence. The CbD analysis of numerous previous attempts to demonstrate contextuality in human judgments shows that all context-dependence in them can be accounted for by direct influences, with no true contextuality present. However, contextual systems in human behavior can be found. In this paper we present a series of crowdsourcing experiments that exhibit true contextuality in simple decision making.}{The design of these experiments is an elaboration of one introduced in the "Snow Queen" experiment (Decision 5, 193-204, 2018), where contextuality was for the first time demonstrated unequivocally.

q-bio.NC↗