Bures volume of the set of mixed quantum states
arXiv:quant-ph/0304041 · doi:10.1088/0305-4470/36/39/308
Abstract
We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the boundary of the set M_N and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N.
15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) corrected