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

Quantum probability in decision making from quantum information representation of neuronal states

The recent wave of interest to modeling the process of decision making with the aid of the quantum formalism gives rise to the following question: ‘How can neurons generate quantum-like statistical data?’ (There is a plenty of such data in cognitive psychology and social science.) Our model is based on quantum-like representation of uncertainty in generation of action potentials. This uncertainty is a consequence of complexity of electrochemical processes in the brain; in particular, uncertainty of triggering an action potential by the membrane potential. Quantum information state spaces can be considered as extensions of classical information spaces corresponding to neural codes; e.g., 0/1, quiescent/firing neural code. The key point is that processing of information by the brain involves superpositions of such states. Another key point is that a neuronal group performing some psychological function F is an open quantum system. It interacts with the surrounding electrochemical environment. The process of decision making is described as decoherence in the basis of eigenstates of F. A decision state is a steady state. This is a linear representation of complex nonlinear dynamics of electrochemical states. Linearity guarantees exponentially fast convergence to the decision state

Application of quantum master equation for long-term prognosis of asset-prices

Abstract This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a "financial bath". The latter is composed of agents' expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents' expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical * Email:[email protected] 1 correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios. Keywords: behavioral finance, decision making, quantum information and probability, violation of Bayesian rationality, open quantum systems

Quantum-like dynamics applied to cognition: a consideration of available options

Quantum probability theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision-making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g. a mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-system extension). We illustrate the relations between these models mathematically and numerically. This article is part of the themed issue 'Second quantum revolution: foundational questions'

Application of Quantum-Markov Open System Models to Human Cognition and Decision

Markov processes, such as random walk models, have been successfully used by cognitive and neural scientists to model human choice behavior and decision time for over 50 years. Recently, quantum walk models have been introduced as an alternative way to model the dynamics of human choice and confidence across time. Empirical evidence points to the need for both types of processes, and open system models provide a way to incorporate them both into a single process. However, some of the constraints required by open system models present challenges for achieving this goal. The purpose of this article is to address these challenges and formulate open system models that have good potential to make important advancements in cognitive science