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Frontiers in Computational Neuroscience

QLCA and Entangled States as Single-Neuron Activity Generators

Yehuda Gavriel Roth

Published Jun 2, 2021• 0 citations
Publisher

Abstract

Each neuron in the central nervous system has many dendrites, which provide input information through impulses. Assuming that a neuron's decision to continue or stop firing is made by rules applied to the dendrites' inputs, we associate neuron activity with a quantum like-cellular automaton (QLCA) concepts. Following a previous study that related the CA description with entangled states, we provide a quantum-like description of neuron activity. After reviewing and presenting the entanglement concept expressed by QLCA terminology, we propose a model that relates quantum-like measurement to consciousness. Then, we present a toy model that reviews the QLCA theory, which is adapted to our terminology. The study also focuses on implementing QLCA formalism to describe a single neuron activity.

DOI
10.3389/fncom.2021.600075

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Each neuron in the central nervous system has many dendrites, which provide input information through impulses. Assuming that a neuron's decision to continue or stop firing is made by rules applied to the dendrites' inputs, we associate neuron activity with a quantum like-cellular automaton (QLCA) concepts. Following a previous study that related the CA description with entangled states, we provide a quantum-like description of neuron activity. After reviewing and presenting the entanglement concept expressed by QLCA terminology, we propose a model that relates quantum-like measurement to consciousness. Then, we present a toy model that reviews the QLCA theory, which is adapted to our terminology. The study also focuses on implementing QLCA formalism to describe a single neuron activity.
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After applying stimulations to the neural network, the neuronal collective state is activated and shows the action potential behavior. We find that this model can generate random neuron-neuron interactions and is proper to describe the process of information transmission in the nervous system physically, which may pave a potential route toward understanding the dynamics of nervous system.
A model of consciousness is proposed, in which the experience attributable to a single neuron is related to its instantaneous firing rate. In that the experience afforded by a sensory neuron can only be quantified within statistical limits from the incidence of spikes across multiple presentations of a stimulus, consciousness remains inaccessible to direct measurement on a single trial. In this way, the model disambiguates subjective experience from objective neural properties. The model adopts a quantum mechanical formalism, in which the state of the neuron is represented as a vector in \nA complex vector space, or as a projector from the space onto that vector. Extension of this formalism to more realistic neural systems merely requires the assimilation of the quantum mechanical principles applicable in this broader context. \nInitially, a mathematical expression for the smooth evolution of a single dimension of perceptual experience will be derived for the single neuron case. \n \nThere follows a description of how the neural state itself might evolve in this \nprocess, utilising the quantum operations formalism of amplitude damping. This approach reveals how smooth evolution of conscious experience might arise from discrete spikes and discontinuous synaptic interaction between neurons. A tensor product formalism will be used to describe the combination of state spaces of individual neurons to form a composite neural space, in which a pure 'mental state' would represent unified conscious experience. The binding of elementary features in this non-local mental state would be reflected in specific patterns of correlated neural firing between remote brain regions. In contrast, the conventional neuron doctrine is classical and local realistic. Local realistic constraints, expressed as Bell Inequalities, limit potential correlations in firing between remote neurons, presenting an opportunity for the experimental test of the scheme in a neurophysiologic thought experiment.
This paper proposes a novel framework for understanding neuronal information processing, suggesting that quantum entanglement plays a significant role in neural communication, termed "quantum neurons." We introduce a model that incorporates quantum superposition and entanglement to simulate neuronal activity, moving beyond classical neuron models. The core mechanism involves utilizing quantum measurements and feedback loops to process information within this quantum neural network. We demonstrate how entangled states can facilitate information transfer exceeding the limitations of classical models, potentially explaining phenomena like consciousness and intelligence. The theoretical framework presented here offers a fundamentally new perspective on the nature of neuronal computation and provides a basis for future research in quantum neuroscience. The primary mathematical concepts explored include quantum state vectors, measurement operators, and the evolution of entangled systems. Key equations and notation are presented below for clarity.
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