Galois Field Quantum Mechanics

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.

9 pages, LaTeX. Uses ws-mplb.cls. Revised title, introduction, and bibliography

References in corpus (4)

• A General Theory of Quantum Relativity
• Time and M-theory
• Background Independent Quantum Mechanics and Gravity
• Bell's Inequalities, Superquantum Correlations, and String Theory

Cited by in corpus (10)

• Discrete Quantum Theories
• Spin and Rotations in Galois Field Quantum Mechanics
• Quantum F_un: the q=1 Limit of Galois Field Quantum Mechanics, Projective Geometry, and the Field with One Element
• Interference and Oscillation in Nambu Quantum Mechanics
• Biorthogonal Quantum Mechanics: Super-Quantum Correlations and Expectation Values without Definite Probabilities
• Spekkens' Toy Model, Finite Field Quantum Mechanics, and the Role of Linearity
• Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations
• A statistical model for quantum spin and photon number states
• Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations
• Is Quantum Gravity a Super-Quantum Theory?