Convex Hulls of Varieties and Entanglement Measures Based on the Roof Construction
| dc.creator | Osborne, Tobias J. | |
| dc.date | 2004-02-06 | |
| dc.date | 2004-03-12 | |
| dc.date.accessioned | 2026-07-07T07:44:53Z | |
| dc.date.available | 2026-07-07T07:44:53Z | |
| dc.description | In this paper we study the problem of calculating the convex hull of certain affine algebraic varieties. As we explain, the motivation for considering this problem is that certain pure-state measures of quantum entanglement, which we call polynomial entanglement measures, can be represented as affine algebraic varieties. We consider the evaluation of certain mixed-state extensions of these polynomial entanglement measures, namely convex and concave roofs. We show that the evaluation of a roof-based mixed-state extension is equivalent to calculating a hyperplane which is multiply tangent to the variety in a number of places equal to the number of terms in an optimal decomposition for the measure. In this way we provide an implicit representation of optimal decompositions for mixed-state entanglement measures based on the roof construction. | |
| dc.description | 23 pages, 3 figures, uses psfrag and amsmath. Fixed conditions for existence of roof | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0402055 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0402055 | |
| dc.identifier | Quantum Information and Computation, vol. 7 (3), pp.209-227 (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123358 | |
| dc.subject | Quantum Physics | |
| dc.title | Convex Hulls of Varieties and Entanglement Measures Based on the Roof Construction | |
| dc.type | text |