On the Bures Volume of Separable Quantum States

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

💡 Research Summary

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The paper establishes quantitative relations between two fundamental measures on the space of quantum states: the Bures volume and the Hilbert‑Schmidt (HS) volume. For any measurable subset (A) of the full set (\mathcal{D}_N) of (N\times N) density matrices, the authors prove the existence of two explicit dimension‑dependent constants (c_1(N)) and (c_2(N)) such that
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