Super-quantum nonlocal correlations in quaternionic quantum theory

Abstract

We consider the nonlocal properties of naive quaternionic quantum theory, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a nonlocal box. This allows one to rule out quaternionic quantum theory using assumptions about communication complexity or information causality while also providing a model for a nonlocal box using familiar structures. © 2011 World Scientific Publishing Company.