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Silver mean conjectures for 15-d volumes and 14-d hyperareas of the separable two-qubit systems | | Paul B. Slater
; | | Date: |
6 Aug 2003 | | Journal: | J. Geometry and Physics 53/1 (2005), 74-97 | | Subject: | quant-ph | | 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 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 s/3, and 10s in terms of (four times) the Kubo-Mori monotone metric. Also, we conjecture, in terms of (four times) the Bures metric, that that part of the 14-dimensional boundary of separable states consisting generically of rank-four 4 x 4 density matrices has volume (``hyperarea’’) 55s/39 and that part composed of rank-three 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 Wigner-Yanase metric (and all other monotone metrics) for rank-four states, the Wigner-Yanase (0.18228) strongly dominates the Bures (0.03982) for the rank-three states. | | Source: | arXiv, quant-ph/0308037 | | Services: | Forum | Review | PDF | Favorites | |
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