192 research outputs found
Geometric information in eight dimensions vs. quantum information
Complementary idempotent paravectors and their ordered compositions, are used
to represent multivector basis elements of geometric Clifford algebra for 3D
Euclidean space as the states of a geometric byte in a given frame of
reference. Two layers of information, available in real numbers, are
distinguished. The first layer is a continuous one. It is used to identify
spatial orientations of similar geometric objects in the same computational
basis. The second layer 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 basis multivectors. 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 for quantum and classical information technologies are discussed.Comment: 14 pages, presented at International Symposium "Quantum Informatics
2007", October 3rd - 5th, 2007, Moscow Zvenigorod, Russi
Separation of Boundary Singularities for Holomorphic Generators
We prove a theorem on separation of boundary null points for generators of
continuous semigroups of holomorphic self-mappings of the unit disk in the
complex plane. Our construction demonstrates the existence and importance of a
particular role of the binary operation given by on generators
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