Quantum Systems Based Upon Galois Fields — From Sub-Quantum to Super-Quantum Correlations

Abstract

In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.

Quantum ${{\mathbb{F}}_{{\rm un}}}$: theq= 1 limit of Galois field quantum mechanics, projective geometry and the field with one element

“…when a measurement is performed on the state represented by the vector  ψ〉 ∈ | q N is given by 6 See also [42][43][44][45][46][47][48][49][50][51][52][53][54][55]. 7 It is possible to define analogs of Hermitian operators using biorthogonal systems.…”