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We first seek the rebit-retrit counterpart to the (formally proven by Lovasand Andai) two-rebit Hilbert-Schmidt separability probability of $\frac{29}{64}=\frac{29}{2^6} \approx 0.453125$ and the qubit-qutrit analogue of the(strongly supported) value of $\frac{8}{33} = \frac{2^3}{3 \cdot 11} \approx0.242424$. We advance the possibilities of a rebit-retrit value of$\frac{860}{6561} =\frac{2^2 \cdot 5 \cdot 43}{3^8} \approx 0.131078$ and aqubit-qutrit one of $\frac{27}{1000} = (\frac{3}{10})^3 =\frac{3^3}{2^3 \cdot5^3} = 0.027$. These four values for $2 \times m$ systems ($m=2,3$) suggestcertain numerator/denominator sequences involving powers of $m$, which wefurther investigate for $m>3$. Additionally, we find that the Hilbert-Schmidtseparability/PPT-probabilities for the two-rebit, rebit-retrit and two-retrit$X$-states all equal $\frac{16}{3 \pi^2} \approx 0.54038$, as well as moregenerally, that the probabilities based on induced measures are equal acrossthese three sets. Then, we extend the master Lovas-Andai formula to inducedmeasures. For instance, the two-qubit function ($k=0$) is$\tilde{\chi}_{2,0}(\varepsilon)=\frac{1}{3} \varepsilon^2 (4 -\varepsilon^2)$,yielding $\frac{8}{33}$, while its $k=1$ induced measure counterpart is$\tilde{\chi}_{2,1}(\varepsilon)=\frac{1}{4} \varepsilon ^2 \left(3-\varepsilon^2\right)^2$, yielding $\frac{61}{143} =\frac{61}{11 \cdot 13} \approx0.426573$, where $\varepsilon$ is a singular-value ratio. Interpolationsbetween Hilbert-Schmidt and operator monotone (Bures, $\sqrt{x}$) measures arealso studied. Using a recently-developed golden-ratio-related (quasirandomsequence) approach, current (significant digits) estimates of the two-rebit andtwo-qubit Bures separability probabilities are 0.15709 and 0.07331,respectively.

Extensions of Generalized Two-Qubit Separability Probability Analyses to Higher Dimensions, Additional Measures and New Methodologies