Minimal Fractal Manifold as Foundation of Quantum Information Theory

Abstract

Derived from the mathematics of the Renormalization Group, the minimal fractal manifold (MFM) represents a spacetime continuum endowed with arbitrarily small deviations from four dimensions (ϵ = 4 - D ≪ 1).  The geometrical structure of the MFM can be conveniently formulated using the concept of dimensional quaternion, a vector-like entity built from component deviations along the four spacetime coordinates. Our analysis shows that dimensional quaternions form a natural basis for qubit systems and Quantum Information Theory.