On the Bures Volume of Separable Quantum States

TL;DR

This paper provides tight bounds on the Bures volume of subsets of quantum states, including separable and positive partial transpose states, using Hilbert-Schmidt volume estimates, with implications for quantum information geometry.

Contribution

It introduces two-sided estimates for the Bures volume of quantum state subsets based on Hilbert-Schmidt volume, improving understanding of quantum state geometry.

Findings

Derived optimal bounds for Bures volume of quantum state sets

Established bounds for separable and PPT states

Enhanced understanding of quantum state volume relationships

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