Hamburg 2009 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 34: Quanteninformation: Konzepte IV
Q 34.6: Vortrag
Mittwoch, 4. März 2009, 15:15–15:30, VMP 6 HS-D
On polynomial invariants of multipartite qubit systems — •Andreas Osterloh1 and Dragomir Ž. Djokovic2 — 1Institut für theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany. — 2Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.
It is a recent observation that entanglement classification for qubits is closely related to local SL(2,C)-invariants including the invariance under qubit permutations, which has been termed SL* invariance. In order to single out the SL* invariants, we analyze the SL(2,C)-invariants of four resp. five qubits and decompose them into irreducible modules for the symmetric group S4 resp. S5 of qubit permutations. A classifying set of measures of genuine multipartite entanglement is given by the ideal of the algebra of SL*-invariants vanishing on arbitrary product states. We find that low degree homogeneous components of this ideal can be constructed in full by using the approach using local invariant operators. Our analysis highlights an intimate connection between this latter procedure and the standard methods to create invariants, such as the Ω-process. As the degrees of invariants increase, the comb based method proves to be particularly efficient.