Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894455 | Journal of Geometry and Physics | 2008 | 23 Pages |
Abstract
We report substantial progress in the study of separability functions and their application to the computation of separability probabilities for the real, complex and quaternionic qubit-qubit and qubit-qutrit systems. We expand our recent work [P.B. Slater, J. Phys. A 39 (2006) 913], in which the Dyson indices of random matrix theory played an essential role, to include the use of not only the volume element of the Hilbert-Schmidt (HS) metric, but also that of the Bures (minimal monotone) metric as measures over these finite-dimensional quantum systems. Further, we now employ the Euler-angle parameterization of density matrices (Ï), in addition to the Bloore parameterization. The Euler-angle separability function for the minimally degenerate complex two-qubit states is well-fitted by the sixth-power of the participation ratio, R(Ï)=1TrÏ2. Additionally, replacing R(Ï) by a simple linear transformation of the Verstraete-Audenaert-De Moor function [F. Verstraete, K. Audenaert, B.D. Moor, Phys. Rev. A 64 (2001) 012316], we find close adherence to Dyson-index behaviour for the real and complex (nondegenerate) two-qubit scenarios. Several of the analyses reported help to fortify our conjectures that the HS and Bures separability probabilities of the complex two-qubit states are 833â0.242424 and 1680(2â1)Ï8â0.733389, respectively. Employing certain regularized beta functions in the role of Euler-angle separability functions, we closely reproduce-consistently with the Dyson-index ansatz-several HS two-qubit separability probability conjectures.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Paul B. Slater,