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Constructing N-qubit entanglement monotones from anti-linear operators

Andreas Osterloh·Jens Siewert
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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 {\em comb} in reference to the {\em hairy-ball theorem}. For qubits (or spin 1/2) the combs are automatically invariant under $SL(2,\CC)$. This implies that the {\em 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-qubit entanglement.

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Andreas Osterloh, Jens Siewert. 2005-03-21. Constructing N-qubit entanglement monotones from anti-linear operators. https://doi.org/10.1103/physreva.72.012337

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