Phys. Rev. A 77, 012316 (2008) [7 pages]Tensor-product versus geometric-product codingReceived 10 September 2007; published 15 January 2008 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. © 2008 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.77.012316
DOI:
10.1103/PhysRevA.77.012316
PACS:
03.67.Lx, 03.65.Ud
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