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.Comment: 22 pages LaTeX. Uses ws-procs975x65.cls. Contribution to the Proceedings of the Conference in Honour of the 90th Birthday of Freeman Dyson, 26-29 August 2013, Institute of Advanced Studies at the Nanyang Technological University, Singapore. Talk presented by Takeuch