Quantum-like states from classical systems

TL;DR

This paper explores how classical systems can be designed to generate quantum-like state spaces using graphs, enabling the simulation of quantum properties such as superposition and entanglement.

Contribution

It introduces a novel graph-based framework for classical systems to mimic quantum states, including an optimized graph product for more compact representations.

Findings

Developed a graph-based model for quantum-like states in classical systems

Extended the theory of QL graphs and their properties

Discussed the potential for classical entanglement in these systems

Abstract

This work studies how a suitably-designed classical system generates with a quantum-like (QL) state space mediated by a graph. The graph plays a special dual role by directing the topology of the classical network and defining a state space that comprises superpositions of states in a tensor product basis. The basis for constructing QL graphs and their properties is reviewed and extended. An optimization of the graph product is developed to produce a more compact graph with the essential properties required to produce states that mimic many of the properties of quantum states. This provides a concrete visualization of the correlation structure in a quantum state space. The question of whether and, if so, how, entanglement can be exhibited by these QL systems is discussed critically and contrasted to the concept of `classical entanglement' in optics.