Canonical Coset Parameterization and the Bures Metric of the Three-level   Quantum Systems
  An explicit parameterization for the state space of an $n$-level density matrix is given. The parameterization is based on the canonical coset decomposition of unitary matrices. We also compute, explicitly, the Bures metric tensor over the state space of two- and three-level quantum systems. 
S. Javad Akhtarshenas