On the Bures Volume of Separable Quantum States

Details On the Bures Volume of Separable Quantum States On the Bures Volume of Separable Quantum States

2009-02-09

arxiv.org/abs/0902.1505v2

JOURNAL OF MATHEMATICAL PHYSICS 50, 083502 (2009)

Physics

Quantum Physics

27 pages. To appear in the Journal of Mathematical Physics

Scientific paper

10.1063/1.3187216

We obtain two sided estimates for the Bures volume of an arbitrary subset of the set of $N\times N$ density matrices, in terms of the Hilbert-Schmidt volume of that subset. For general subsets, our results are essentially optimal (for large $N$). As applications, we derive in particular nontrivial lower and upper bounds for the Bures volume of sets of separable states and for sets of states with positive partial transpose. PACS numbers: 02.40.Ft, 03.65.Db, 03.65.Ud, 03.67.Mn

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