Tensor-product vs. geometric-product coding
arXiv:0709.1268 · doi:10.1103/PhysRevA.77.012316
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, GHZ, and Hadamard states are visualized by means of colored oriented polylines.
6 eps figures
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Cited by in corpus (7)
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- A Geometric Algebra Perspective On Quantum Computational Gates And Universality In Quantum Computing
- A Case for Applying an Abstracted Quantum Formalism to Cognition
- A loophole of all `loophole-free' Bell-type theorems
- Teleportation of geometric structures in 3D
- Quantum Computation via Sparse Distributed Representation
- Geometric Algebra Model of Distributed Representations