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Entanglement of localized states

O. Giraud, J. Martin, B. Georgeot

par Bertrand Georgeot - 3 mai 2007

We derive exact expressions for the mean value of Meyer-Wallach entanglement Q for localized random vectors. For vectors localized on a randomly chosen subset of the basis, the mean Q tends for large system sizes to a constant which depends on the participation ratio, whereas for vectors localized on adjacent basis states it goes to zero as a constant over the number of qubits. Applications to many-body systems and Anderson localization are discussed.