Geometric information in eight dimensions vs. quantum information

摘要

Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basiselements of geometric Clifford algebra G_(3,0)as the states of a geometric byte in given frame of reference. Twolayers of information, available in real numbers, are distinguished. The first layer is a continuous one. It isused to identify spatial orientations of similar geometric objects in the same computational basis. The secondlayer is a binary one. It is used to manipulate with 8D structure elements inside the computational basis itself.An oriented unit cube representation, rather than a matrix one, is used to visualize an inner structure of basismultivectors. Both layers of information are used to describe unitary operations — reflections and rotations in Euclidian and Hilbert spaces. The results are compared with ones for quantum gates. Some consequences forquantum and classical information technologies are discussed.