Geometric algebra in quantum information processing

This paper presents an intuitive geometric model for multiqubit quantum systems, which is formulated using geometric (aka Clifford) algebras. First, it is shown how Euclidean spinors may be interpreted as entities in the geometric algebra of a Euclidean vector space. Second, it is shown how this entire formalism lifts naturally to Minkowski space-time and its associated geometric algebra, and that this provides insights into how density operators and entanglement behave under Lorentz transformations. Third, the utility of geometric algebra in understanding both unitary and nonunitary quantum operations is demonstrated by means of examples of contemporary interest in quantum information processing.

T.F. Havel and C.J.L. Doran, Geometric algebra in quantum information processing, In S. Lomonaco, ed. Quantum Computation and Quantum Information Science. AMS Contemporary Math series (2000)