Hannover 2010 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 4: Quantum Information: Concepts and Methods I

Q 4.5: Talk

Monday, March 8, 2010, 15:00–15:15, E 214

Convex Polytopes and Quantum States — •colin wilmott, hermann kampermann, and dagmar bruss — Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Düsseldorf

A convex polytope is defined as the convex hull of a finite non-empty set of vectors. We present a theorem of Rado (1952) which characterizes the convex hull of the collection of all permutations of a given real d-tuple in terms of the Hardy-Littlewood-Pólya spectral order relation ≺. We give a necessary and sufficient condition to construct a d-dimensional convex polytope which utilizes Rado’s original (d−1)-dimensional characterization, and we describe how the resulting polytope may be placed in a quantum mechanical framework.