Geometric Algebra in Quantum Information Processing

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dc.creatorHavel, Timothy F.
dc.creatorDoran, Chris J. L.
dc.date2000-04-07
dc.date2001-06-27
dc.date.accessioned2026-07-07T05:59:50Z
dc.date.available2026-07-07T05:59:50Z
dc.descriptionThis 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.
dc.description27 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
dc.identifierhttps://arxiv.org/abs/quant-ph/0004031
dc.identifierhttp://arxiv.org/abs/quant-ph/0004031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/88829
dc.subjectQuantum Physics
dc.titleGeometric Algebra in Quantum Information Processing
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