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Proceedings Paper

Geometric information in eight dimensions vs. quantum information
Author(s): Victor I. Tarkhanov; Michael M. Nesterov
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Paper Abstract

Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basis elements of geometric Clifford algebra G3,0 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.

Paper Details

Date Published: 29 April 2008
PDF: 14 pages
Proc. SPIE 7023, Quantum Informatics 2007, 70230J (29 April 2008); doi: 10.1117/12.801913
Show Author Affiliations
Victor I. Tarkhanov, St. Petersburg State Polytechnic Univ. (Russia)
Michael M. Nesterov, St. Petersburg Institute for Informatics and Automation (Russia)

Published in SPIE Proceedings Vol. 7023:
Quantum Informatics 2007

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