Alladi Ramakrishnan Hall

Towards a generalization of W-states

Andreas Osterloh

Institute for Theoretical Physics, University of Duisburg-Essen, Duisburg, Germany

States possessing only three-tangle but distributed all over four qubits are singled out. This is an analogue of states from the three-qubit $W$-class exclusively
possessing globally distributed pairwise entanglement as measured by the concurrence. We perform an analysis for four qubits, showing that such a state indeed exists and obtain the exact solution to their convex-roof of the three-tangle. 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.