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Silver mean conjectures for 15d volumes and 14d hyperareas of the separable twoqubit systems  Paul B. Slater
;  Date: 
6 Aug 2003  Journal:  J. Geometry and Physics 53/1 (2005), 7497  Subject:  quantph  Affiliation:  University of California  Abstract:  Extensive numerical integration results lead us to conjecture that the silver mean, that is, s = sqrt{2}1 = .414214 plays a fundamental role in certain geometries (those given by monotone metrics) imposable on the 15dimensional convex set of twoqubit systems. For example, we hypothesize that the volume of separable twoqubit states, as measured in terms of (four times) the minimal monotone or Bures metric is s/3, and 10s in terms of (four times) the KuboMori monotone metric. Also, we conjecture, in terms of (four times) the Bures metric, that that part of the 14dimensional boundary of separable states consisting generically of rankfour 4 x 4 density matrices has volume (``hyperarea’’) 55s/39 and that part composed of rankthree density matrices, 43s/39, so the total boundary hyperarea would be 98s/39. While the Bures probability of separability (0.07334) dominates that (0.050339) based on the WignerYanase metric (and all other monotone metrics) for rankfour states, the WignerYanase (0.18228) strongly dominates the Bures (0.03982) for the rankthree states.  Source:  arXiv, quantph/0308037  Services:  Forum  Review  PDF  Favorites 


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