Galois Field Quantum Mechanics

TL;DR

This paper develops a discrete quantum mechanics framework over Galois fields, revealing correlations that do not violate Bell's inequality, challenging traditional notions of quantum nonlocality.

Contribution

It introduces a novel discrete quantum mechanics model over Galois fields that exhibits unique correlation properties.

Findings

Correlations do not violate CHSH Bell's inequality.

Discrete quantum mechanics cannot be reproduced by hidden variable theories.

Model provides new insights into quantum correlations over finite fields.

Abstract

We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.