  Every choice of an orthonormal frame in the d-dimensional Hilbert space of a
system corresponds to one set of all mutually commuting density matrices or,
equivalently, a classical statistical state space of the system; the quantum
state space itself can thus be profitably viewed as an SU(d) orbit of classical
state spaces, one for each orthonormal frame. We exploit this connection to
study the relative volume of separable states of a bipartite quantum system.
While the two-qubit case is studied in considerable analytic detail, for higher
dimensional systems we fall back on Monte Carlo. Several new insights seem to
emerge from our study.
