Bures volume of the set of mixed quantum states
Abstract
We compute the volume of the N2-1 dimensional set MN of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R4. We find also the area of the boundary of the set MN 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.
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