On the Bures Volume of Separable Quantum States

Abstract

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

27 pages. To appear in the Journal of Mathematical Physics

References in corpus (1)

• The volume of separable states is super-doubly-exponentially small

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