Quantum features of natural cellular automata

Abstract

Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws. The class of "natural" Hamiltonian cellular automata is based exclusively on integer-valued variables and couplings and their dynamics derives from an Action Principle. They can be mapped reversibly to continuum models by applying Sampling Theory. Thus, "deformed" quantum mechanical models with a finite discreteness scale $l$ are obtained, which for $l\to 0$ reproduce familiar continuum results. We have recently demonstrated that such automata can form "multipartite" systems consistently with the tensor product structures of nonrelativistic many-body quantum mechanics, while interacting and maintaining the linear evolution. Consequently, the Superposition Principle fully applies for such primitive discrete deterministic automata and their composites and can produce the essential quantum effects of interference and entanglement.

9 pages; based on invited talk at the symposium on "Emergent Quantum Mechanics" (EmQM15, Vienna, October 2015)

References in corpus (6)

• Spacetime could be simultaneously continuous and discrete in the same way that information can
• Dissipation and quantization for composite systems
• Quantumness of discrete Hamiltonian cellular automata
• Are nonlinear discrete cellular automata compatible with quantum mechanics?
• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata
• The ideal energy of classical lattice dynamics

Cited by in corpus (1)

• Non-local imprints of gravity on quantum theory