Geometric Algebra in Quantum Information Processing

  • Havel T
  • Doran C
ISSN: 0308-0110
N/ACitations
Citations of this article
40Readers
Mendeley users who have this article in their library.

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.

Cite

CITATION STYLE

APA

Havel, T. F., & Doran, C. J. L. (2000). Geometric Algebra in Quantum Information Processing. Quantum Information Processing, 0000, 27. Retrieved from http://arxiv.org/abs/quant-ph/0004031

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free