
Physics 2004
A BlochSphereType Model for Two Qubits in the Geometric Algebra of a 6D Euclidean Vector SpaceDOI: 10.1117/12.540929 Abstract: Geometric algebra is a mathematical structure that is inherent in any metric vector space, and defined by the requirement that the metric tensor is given by the scalar part of the product of vectors. It provides a natural framework in which to represent the classical groups as subgroups of rotation groups, and similarly their Lie algebras. In this article we show how the geometric algebra of a sixdimensional real Euclidean vector space naturally allows one to construct the special unitary group on a twoqubit (quantum bit) Hilbert space, in a fashion similar to that used in the wellestablished Bloch sphere model for a single qubit. This is then used to illustrate the Cartan decompositions and subalgebras of the fourdimensional special unitary group, which have recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev. A 67, 042313, 2003] to study the entangling capabilities of twoqubit unitaries.
