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The generic real (b=1) and complex (b=2) two-qubit states are 9-dimensionaland 15-dimensional in nature, respectively. The total volumes of the spacesthey occupy with respect to the Hilbert-Schmidt and Bures metrics areobtainable as special cases of formulas of Zyczkowski and Sommers. We claimthat if one could determine certain metric-independent 3-dimensional"eigenvalue-parameterized separability functions" (EPSFs), then these formulascould be readily modified so as to yield the Hilbert-Schmidt and Bures volumesoccupied by only the separable two-qubit states (and hence associatedseparability probabilities). Motivated by analogous earlier analyses of"diagonal-entry-parameterized separability functions", we further explore thepossibility that such 3-dimensional EPSFs might, in turn, be expressible asunivariate functions of some special relevant variable--which we hypothesize tobe the maximal concurrence (0 < C <1) over spectral orbits. Extensive numericalresults we obtain are rather closely supportive of this hypothesis. Both thereal and complex estimated EPSFs exhibit clearly pronounced jumps of magnituderoughly 50% at C=1/2, as well as a number of additional matchingdiscontinuities.

Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence