Dyson-Index-Like Behavior of Bures Separability Functions

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dc.creatorSlater, Paul B.
dc.date2007-08-30
dc.date.accessioned2026-07-07T08:26:43Z
dc.date.available2026-07-07T08:26:43Z
dc.descriptionWe conduct a study based on the Bures (minimal monotone) metric, analogous to that recently reported for the Hilbert-Schmidt (flat or Euclidean) metric (arXiv:0704.3723v2). Among the interesting results obtained there had been proportionalities--in exact correspondence to the Dyson indices β= 1, 2, 4 of random matrix theory--between the fourth, second and first powers of the separability functions S_{type}(μ) for real, complex and quaternionic qubit-qubit scenarios, Here μ=\sqrt{\frac{ρ_{11} ρ_{44}}{ρ_{22} ρ_{33}}}, with ρbeing a 4 x 4 density matrix. Separability functions have proved useful--in the framework of the Bloore (correlation coefficient/off-diagonal scaling) parameterization of density matrices--for the calculation of separability probabilities. We find--for certain, basic simple scenarios (in which the diagonal entries of ρare unrestricted, and one or two off-diagonal [real, complex or quaternionic] pairs of entries are nonzero) --that these proportionalities no longer strictly hold in the Bures case, but do come remarkably close to holding.
dc.description13 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0708.4208
dc.identifierhttp://arxiv.org/abs/0708.4208
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137037
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject81P05; 52A38; 15A90; 28A75
dc.titleDyson-Index-Like Behavior of Bures Separability Functions
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