Hilbert–Schmidt volume of the set of mixed quantum states
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چکیده
We compute the volume of the convex (N2−1)-dimensional set MN of density matrices of size N with respect to the Hilbert–Schmidt measure. The hyperarea of the boundary of this set is also found and its ratio to the volume provides information about the structure of MN . Similar investigations are also performed for the smaller set of all real density matrices. As an intermediate step, we analyse volumes of the unitary and orthogonal groups and of the flag manifolds. PACS number: 03.65.Ta
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تاریخ انتشار 2003