Quantum-like states on complex synchronized networks

Abstract

Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (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 like 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.

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• Coupling quantum-like cognition with the neuronal networks within generalized probability theory
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• Quantum-like product states constructed from classical networks
• Quantum-like representation of neuronal networks' activity: modeling "mental entanglement"
• Dynamics in an emergent quantum-like state space generated by a nonlinear classical network
• Collective motion from quantum-inspired dynamics in visual perception