Bures volume of the set of mixed quantum states

Details Bures volume of the set of mixed quantum states Bures volume of the set of mixed quantum states

2003-04-04

arxiv.org/abs/quant-ph/0304041v3

J. Phys. A 36, 10083-10100 (2003)

Physics

Quantum Physics

15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) corrected

Scientific paper

10.1088/0305-4470/36/39/308

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.

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