arXiv:0709.1268 · Physical Review A

Tensor-product versus geometric-product coding

Diederik Aerts, Marek Czachor

Published Jan 15, 2008• 17 citations

Abstract

Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is analogous to quantum computation but does not involve quantum mechanics. We discuss in detail similarities and differences between the two approaches and illustrate the formulas by explicit geometric objects where multivector versions of the Bell-basis, Greenberger-Horne-Zeilinger, and Hadamard states are visualized by means of colored oriented polylines.

DOI: 10.1103/physreva.77.012316

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