Proceedings of the International Workshop "Quantum Entanglement in Physical and Information Sciences" Centro di Ricerca Matematica Ennio DeGiorgi, Scuola Normale Superiore; December 14—18, 2004, Pisa, Italy – Eds. C. Macchiavello, R. Fazio and G. M. PalmaNo Access

ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS

ANDREAS OSTERLOH

Institut für Theoretische Physik, Universität Hannover, D-30167 Hannover, Germany

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and

JENS SIEWERT

MATIS-INFM & Dipartimento di Metodologie Fisiche e Chimiche (DMFCI), viale A. Doria 6, 95125 Catania, Italy

Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

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https://doi.org/10.1142/S0219749906001980Cited by:81 (Source: Crossref)

Abstract

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem. For qubits (i.e. spin 1/2) the combs are automatically invariant under SL (2, ℂ). This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.

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