Spin and Rotations in Galois Field Quantum Mechanics
Lay Nam Chang, Zachary Lewis, Djordje Minic, Tatsu Takeuchi
TL;DR
This paper explores the properties of Galois Field Quantum Mechanics, focusing on spin-like systems, rotations, and correlations, revealing that CHSH inequality is not violated within this finite field framework.
Contribution
It introduces a model of quantum mechanics over GF(q) that incorporates spin and rotation analogs, and analyzes two-particle correlations without violating CHSH inequality.
Findings
SO(3) rotations can be represented in GF(q) quantum systems
Two-particle correlations do not violate CHSH inequality
Galois Field Quantum Mechanics exhibits unique spin and rotation properties
Abstract
We discuss the properties of Galois Field Quantum Mechanics constructed on a vector space over the finite Galois field GF(q). In particular, we look at 2-level systems analogous to spin, and discuss how SO(3) rotations could be embodied in such a system. We also consider two-particle `spin' correlations and show that the Clauser-Horne-Shimony-Holt (CHSH) inequality is nonetheless not violated in this model.
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