Volumes and hyperareas of the spaces of separable and nonseparable qubit-qutrit systems: Initial numerical analyses
| dc.creator | Slater, Paul B. | |
| dc.date | 2004-05-20 | |
| dc.date.accessioned | 2026-07-07T06:09:46Z | |
| dc.date.available | 2026-07-07T06:09:46Z | |
| dc.description | Paralleling our recent computationally-intensive work for the case N=4 (quant-ph/0308037), we undertake the task for N=6 of computing to high numerical accuracy, the formulas of Sommers and Zyczkowski (quant-ph/0304041) for the (N^2-1)-dimensional volume and (N^2-2)-dimensional hyperarea of the (separable and nonseparable) N x N density matrices, based on the Bures (minimal monotone) metric. At the same time, we estimate the unknown volumes and hyperareas based on a number of other monotone metrics of interest. Additionally, we estimate -- but with perhaps unavoidably diminished accuracy -- all these volume and hyperarea quantities, when restricted to the ``small'' subset of 6 x 6 density matrices that are separable (classically correlated) in nature. The ratios of separable to separable plus nonseparable volumes, then, yield corresponding estimates of the ``probabilities of separability''. We are particularly interested in exploring the possibility that a number of the various 35-dimensional volumes and 34-dimensional hyperareas, possess exact values -- which we had, in fact, conjectured to be the case for the qubit-qubit systems (N=4), with the ``silver mean'', sqrt{2}-1, appearing to play a fundamental role as regards the separable states. | |
| dc.description | 12 pages, 7 tables | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0405114 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0405114 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92070 | |
| dc.subject | Quantum Physics | |
| dc.title | Volumes and hyperareas of the spaces of separable and nonseparable qubit-qutrit systems: Initial numerical analyses | |
| dc.type | text |