Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence

Details Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence Two-Qubit Separabilities as Piecewise Continuous Functions of Maximal Concurrence

2008-06-20

arxiv.org/abs/0806.3294v3

J. Phys. A: Math. Theor. 41 No 50 (19 December 2008) 505303

Physics

Quantum Physics

12 pages, 7 figures, new abstract, revised for J. Phys. A

Scientific paper

10.1088/1751-8113/41/50/505303

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

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