Regensburg 2007 – scientific programme
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SYEN: Symposium Entanglement
SYEN 1: Symposium Entanglement
SYEN 1.4: Invited Talk
Thursday, March 29, 2007, 15:30–16:00, H1
Towards the convex roof of multipartite entanglement measures — •Andreas Osterloh1, Jens Siewert2, Robert Lohmayer2, and Armin Uhlmann3 — 1Institut für Theoretische Physik, Leibniz Universität Hannover, D-30167 Hannover, Germany — 2Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany — 3Institut für Theoretische Physik, Universität Leipzig, D-04109 Leipzig, Germany
Selective measures for genuine multipartite entanglement of pure states have been presented recently. Their extension to mixed states via the convex roof is approached starting from the three-tangle. We provide a thorough analysis of mixed three-qubit states composed of a GHZ state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. From our studies we derive an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. This result can be generalized for N-tangles of rank-2 N-qubit states (N≥ 3).
References:
A. Osterloh and J. Siewert, e-print quant-ph/0506073 Int. J. Quant. Inf. 4, 531 (2006).
R. Lohmayer, A. Osterloh, J. Siewert, A. Uhlmann, e-print quant-ph/0606071, Phys. Rev. Lett. 97, 260502 (2006).