  Jakobczyk and Siennicki studied two-dimensional sections of a set of
(generalized) Bloch vectors corresponding to n x n density matrices of
two-qubit systems (that is, the case n = 4). They found essentially five
different types of (nontrivial) separability regimes. We compute the
Euclidean/Hilbert-Schmidt (HS) separability probabilities assigned to these
regimes, and conduct parallel two-dimensional sectional analyses for the
higher-level cases n=6,8,9 and 10. Making use of the newly-introduced
capability for integration over implicitly defined regions of version 5.1 of
Mathematica -- also fruitfully used in our n=4 three-parameter
entropy-maximization-based study quant-ph/0507203 -- we obtain a wide-ranging
variety of exact HS-probabilities. For n>6, the probabilities are those of
having a partial positive transpose (PPT). For the n=6 case, we also obtain
biseparability probabilities; in the n=8,9 instances, bi-PPT probabilities; and
for n=8, tri-PPT probabilities. By far, the most frequently recorded
probability for n>4 is \pi/4 = 0.785398. We also conduct a number of related
analyses, pertaining to the (one-dimensional) boundaries (both exterior and
interior) of the separability and PPT domains, and attempt (with limited
success) some exact calculations pertaining to the 9-dimensional (real) and
15-dimensional (complex) convex sets of two-qubit density matrices -- for which
HS-separability probabilities have been conjectured, but not verified.
