Quantum state evolution in C2 and G3+

Abstract

It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on generalization of formal, unspecified, complex plane to arbitrary variable, but explicitly defined, planes in 3D, and of usual Hopf fibration to maps generated by arbitrary unit value bivectors. Analysis of the new structure demonstrates that quantum state evolution in terms of two dimensional complex space gives only restricted information compared to that in even geometric algebra.