Hilbert--Schmidt volume of the set of mixed quantum states

Details Hilbert--Schmidt volume of the set of mixed quantum states Hilbert--Schmidt volume of the set of mixed quantum states

2003-02-27

arxiv.org/abs/quant-ph/0302197v3

J. Phys. A 36, 10115-10130 (2003)

Physics

Quantum Physics

13 revtex pages, ver 3: minor improvements

Scientific paper

10.1088/0305-4470/36/39/310

We compute the volume of the convex N^2-1 dimensional set M_N of density matrices of size N with respect to the Hilbert-Schmidt measure. The hyper--area of the boundary of this set is also found and its ratio to the volume provides an information about the complex structure of M_N. Similar investigations are also performed for the smaller set of all real density matrices. As an intermediate step we analyze volumes of the unitary and orthogonal groups and of the flag manifolds.

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