Qubit exchange interactions from permutations of classical bits

Abstract

In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by 't Hooft. Our result illustrates a new Baker-Campbell-Hausdorff formula with terminating series expansion.

14 pages; accepted and to appear in Int. J. Qu. Info. (IJQI)

References in corpus (7)

• Quantum theory from rules on information acquisition
• Dissipation and quantization for composite systems
• Quantumness of discrete Hamiltonian cellular automata
• Probability theory as a physical theory points to superdeterminism
• Some considerations on Determinism and Free Will
• The linearity of quantum mechanics from the perspective of Hamiltonian cellular automata
• Ontological states and dynamics of discrete (pre-)quantum systems

Cited by in corpus (4)

• Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics
• Are quantum spins but small perturbations of ontological Ising spins?
• Are Quantum-Classical Hybrids compatible with Ontological Cellular Automata?
• Does Quantum Mechanics Breed Larger, More Intricate Quantum Theories? The Case for Experience-Centric Quantum Theory and the Interactome of Quantum Theories