  Paralleling our recent computationally-intensive work for the case N=4
(quant-ph/0308037), we undertake the task for N=6 of computing to high
numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041)
for the (N^2-1)-dimensional volume and (N^2-2)-dimensional hyperarea of the
(separable and nonseparable) N x N density matrices, based on the Bures
(minimal monotone) metric. At the same time, we estimate the unknown volumes
and hyperareas based on a number of other monotone metrics of interest.
Additionally, we estimate -- but with perhaps unavoidably diminished accuracy
-- all these volume and hyperarea quantities, when restricted to the ``small''
subset of 6 x 6 density matrices that are separable (classically correlated) in
nature. The ratios of separable to separable plus nonseparable volumes, then,
yield corresponding estimates of the ``probabilities of separability''. We are
particularly interested in exploring the possibility that a number of the
various 35-dimensional volumes and 34-dimensional hyperareas, possess exact
values -- which we had, in fact, conjectured to be the case for the qubit-qubit
systems (N=4), with the ``silver mean'', sqrt{2}-1, appearing to play a
fundamental role as regards the separable states.

Quantum Physics