Some Applications for an Euler Angle Parameterization of SU(N) and U(N)

Abstract

Here we apply our SU(N) and U(N) parameterizations to the question of entanglement in the two qubit and qubit/qutrit system. In particular, the group operations which entangle a two qubit pure state will be given, as well as the corresponding manifold that the operations parameterize. We also give the volume of this manifold, as well as the hypothesized volume for the set of all entangled two qubit pure and mixed states. Extension of this work to the qubit/qutrit system will also be given.