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Employing the volume of quantum steering ellipsoids (QSEs) as a measure onthe fifteen-dimensional convex set of two-qubit states, we estimate the ratioof the integral of the measure over the separable states to its integral overall (separable and entangled) states to be 0.0288. This can be contrasted withthe considerably larger separability ratios (probabilities) of $\frac{8}{33} =\frac{2^3}{3 \cdot 11} \approx 0.242424$ and $\frac{25}{341}=\frac{5^2}{11\cdot 31} \approx 0.0733138$ that various forms of evidence point to with theuse of the prominent Hilbert-Schmidt and Bures measures, respectively. Thequestions of whether the ratio in the QSE setting can be more preciselyobtained or even exactly computed, as well as whether a metric can beconstructed, the volume element of which yields the measure, remain to beaddressed. We also investigate related issues pertaining to absoluteseparability. Further, we examine the behavior of the separabilityprobability--constant in the Hilbert-Schmidt case and decreasing in theBures--as a function of the Bloch vector norm in the QSE instance. It appearsto increase approaching the pure state boundary.

Quantum Steering Ellipsoid Volume as a Measure on the Two-Qubit States and Associated Separability and Absolute Separability Ratios