2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137037We 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.13 pages, 2 figuresMathematical PhysicsQuantum Physics81P05; 52A38; 15A90; 28A75text