Bures measures over the spaces of two- and three-dimensional density matrices

Due to considerable recent interest in the: use of density matrices for a w ide variety of purposes, including quantum computation, we present a genera l method for their parameterizations in terms of Euler angles. We assert th at this is of more fundamental importance than las several people have rema rked to us) "just another parameterization of the density matrix". There ar e several uses to which this methodology can be put. One that has received particular attention is in the construction of certain distinguished (Bures ) measures on the (n(2) - 1)-dimensional convex sets of n x n density matri ces. (C) 2001 Elsevier Science B.V. All rights reserved.