Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10735181 | Journal of Geometry and Physics | 2005 | 24 Pages |
Abstract
Extensive numerical integration results lead us to conjecture that the silver mean, that is, ÏAg=2â1â0.414214 plays a fundamental role in certain geometries (those given by monotone metrics) imposable on the 15-dimensional convex set of two-qubit systems. For example, we hypothesize that the volume of separable two-qubit states, as measured in terms of (four times) the minimal monotone or Bures metric is ÏAg/3 , and 10ÏAg in terms of (four times) the Kubo-Mori monotone metric. Also, we conjecture, in terms of (four times) the Bures metric, that part of the 14-dimensional boundary of separable states consisting generically of rank-four4Ã4 density matrices has volume (“hyperarea”) 55ÏAg/39 , and that part composed of rank-three density matrices, 43ÏAg/39 , so the total boundary hyperarea would be 98ÏAg/39 . While the Bures probability of separability (â 0.07334) dominates that (â 0.050339) based on the Wigner-Yanase metric (and all other monotone metrics) for rank-four states, the Wigner-Yanase (â 0.18228) strongly dominates the Bures (â 0.03982) for the rank-three states.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Paul B. Slater,