Extended Studies of Separability Functions and Probabilities and the Relevance of Dyson Indices
| dc.creator | Slater, Paul B. | |
| dc.date | 2008-02-01 | |
| dc.date.accessioned | 2026-07-07T09:59:32Z | |
| dc.date.available | 2026-07-07T09:59:32Z | |
| dc.description | 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 (arXiv:0704.3723), 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 (rho), 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(rho)=1/Tr(rho)^2. Additionally, replacing R(rho) by a simple linear transformation of the Verstraete-Audenaert-De Moor function (arXiv:quant-oh/0011111), we find close adherence to Dyson-index behavior 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 8/33 = 0.242424 and 1680 (sqrt{2}-1)/pi^8 = 0.733389, 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. | |
| dc.description | 45 pages, 23 figures | |
| dc.identifier | https://arxiv.org/abs/0802.0197 | |
| dc.identifier | http://arxiv.org/abs/0802.0197 | |
| dc.identifier | J. Geom. Phys. 58 (2008), 1101-1123 | |
| dc.identifier | doi:10.1016/j.geomphys.2008.03.014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168058 | |
| dc.subject | Quantum Physics | |
| dc.subject | Mathematical Physics | |
| dc.title | Extended Studies of Separability Functions and Probabilities and the Relevance of Dyson Indices | |
| dc.type | text |