Quantum features of natural cellular automata
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by
Hans-Thomas Elze
2016
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→ 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.
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