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Geometric Algebra in Quantum Information Processing
Timothy F. Havel, Chris J. L. Doran
abstract: This paper develops a geometric model for coupled two-state quantum systems
(qubits), which is formulated using geometric (aka Clifford) algebra. It begins
by showing how Euclidean spinors can be interpreted as entities in the
geometric algebra of a Euclidean vector space. This algebra is then lifted to
Minkowski space-time and its associated geometric algebra, and the insights
this provides into how density operators and entanglement behave under Lorentz
transformations are discussed. The direct sum of multiple copies of space-time
induces a tensor product structure on the associated algebra, in which a
suitable quotient is isomorphic to the matrix algebra conventionally used in
multi-qubit quantum mechanics. Finally, the utility of geometric algebra in
understanding both unitary and nonunitary quantum operations is demonstrated on
several examples of interest in quantum information processing.
- oai_identifier:
- oai:arXiv.org:quant-ph/0004031
- categories:
- quant-ph
- comments:
- 27 pages, AMS conm-p-l documentclass, to be published in the AMS
``Contemporary Math'' series volume entitled Quantum Computation and Quantum
Information Science (S. Lomonaco, ed.); version 3 includes minor corrections
and was reformatted single-spaced for publisher
- arxiv_id:
- quant-ph/0004031
- created:
- 2000-04-07
- updated:
- 2001-06-27
Full article ▸
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