Details
Originalsprache | Englisch |
---|---|
Seiten (von - bis) | 209-227 |
Seitenumfang | 19 |
Fachzeitschrift | Quantum Information and Computation |
Jahrgang | 7 |
Ausgabenummer | 3 |
Publikationsstatus | Veröffentlicht - März 2007 |
Extern publiziert | Ja |
Abstract
In this paper we study the problem of calculating the convex hull of certain a ne 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 a ne 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Physik und Astronomie (insg.)
- Kern- und Hochenergiephysik
- Mathematik (insg.)
- Mathematische Physik
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Informatik (insg.)
- Theoretische Informatik und Mathematik
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in: Quantum Information and Computation, Jahrgang 7, Nr. 3, 03.2007, S. 209-227.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Convex hulls of varieties and entanglement measures based on the roof construction
AU - Osborne, Tobias J.
N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2007/3
Y1 - 2007/3
N2 - In this paper we study the problem of calculating the convex hull of certain a ne 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 a ne 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.
AB - In this paper we study the problem of calculating the convex hull of certain a ne 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 a ne 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.
KW - Algebraic geometry
KW - Entanglement measures
UR - http://www.scopus.com/inward/record.url?scp=34247253919&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:34247253919
VL - 7
SP - 209
EP - 227
JO - Quantum Information and Computation
JF - Quantum Information and Computation
SN - 1533-7146
IS - 3
ER -