Univariate Functions for the Hilbert-Schmidt Volumes of the Real and Complex Separable Two-Qubit Systems

Details Univariate Functions for the Hilbert-Schmidt Volumes of the Real and Complex Separable Two-Qubit Systems Univariate Functions for the Hilbert-Schmidt Volumes of the Real and Complex Separable Two-Qubit Systems

2006-07-28

arxiv.org/abs/quant-ph/0607209v1

Physics

Quantum Physics

14 pages, 6 figures

Scientific paper

The (complex) two-qubit systems comprise a 15-dimensional convex set and the real two-qubit systems, a 9-dimensional convex set. While formulas for the Hilbert-Schmidt volumes of these two sets are known -- owing to recent important work of Sommers and Zyczkowski (J. Phys. A {36}, 10115 [2003]) -- formulas have not been so far obtained for the volumes of the separable subsets. We reduce these two problems to the determination of certain functions of a single variable.

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