Entangled quantum states in a local deterministic theory

TL;DR

This paper explores how certain local deterministic models can be described using quantum operators, forming a quantum field theory that admits entangled states, challenging traditional views on Bell's inequalities.

Contribution

It demonstrates that local deterministic models can be represented as quantum field theories with entangled states, questioning the assumption that such models cannot violate Bell's inequalities.

Findings

Quantum operators describe long-distance behavior of cellular automata-like models.

Entangled states can be constructed exactly within these models.

The models may allow Bell's inequalities to be violated despite being local and deterministic.

Abstract

Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a model into a genuine quantum field theory, obeying the usual conditions of locality in terms of its quantum commutators. Entangled states can be constructed exactly as in quantum theories. This raises the question whether such models allow Bell's inequalities to be violated. Being a local, deterministic theory, one would argue that this is impossible, but since at large distance scales the model does not seem to differ from real quantum field theories, there is reason to wonder why it should not allow entangled states. The standard arguments concerning Bell's inequalities are re-examined in this light.