Rostock 2019 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 59: Quantum Information (Concepts and Methods) V

Q 59.6: Vortrag

Freitag, 15. März 2019, 11:45–12:00, S HS 001 Chemie

Generalized W-state of four qubits with exclusively threetangle — Sebastian Gartzke and •Andreas Osterloh — Universität Duisburg-Essen, Lotharstrasse 1, 47057 Duisburg

We single out a class of states possessing only threetangle but distributed all over four qubits. This is a three-site analogue of states from the W-class, which only possess globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists. To this end we analyze specific states of four qubits that are not convexly balanced as for SL invariant families of entanglement, but only affinely balanced. For these states all possible SL-invariants vanish, hence they are part of the SL null-cone. Instead, they will possess at least a certain unitary invariant. As an interesting byproduct it is demonstrated that the exact convex roof is reached in the rank-two case of a homogeneous polynomial SL-invariant measure of entanglement of degree 2m, if there is a state which corresponds to a maximally m-fold degenerate solution in the zero-polytope that can be combined with the convexified minimal characteristic curve to give a decomposition of the density matrix. If more than one such state does exist in the zero polytope, a minimization must be performed. A better lower bound than the lowest convexified characteristic curve is obtained if no decomposition of the mixed state is obtained in this way.