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Two-Qubit Separability Probabilities and Beta Functions | | Paul B. Slater
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1 Sep 2006 | | Abstract: | Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest case of n=4, that is, the two-qubit systems. We find that the two functions of principal interest that require determination can be well approximated --if not actually fit entirely -- by certain beta functions. | | Source: | arXiv, quant-ph/0609006 | | Services: | Forum | Review | PDF | Favorites | |
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