  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.
