Collective multipole-like signatures of entanglement in symmetric N-qubit systems

Abstract

A cogent theory of collective multipole-like quantum correlations in symmetric multiqubit states is presented by employing SO(3) irreducible spherical tensor representation. An arbitrary bipartite division of this system leads to a family of inequalities to detect entanglement involving averages of these tensors expressed in terms of the total system angular momentum operator. Implications of this theory to the quantum nature of multipole-like correlations of all orders in the Dicke states are deduced. A selected set of examples illustrate these collective tests. Such tests detect entanglement in macroscopic atomic ensembles, where individual atoms are not accessible.

REVTEX, 4 pages with 1 figure; To appear in Phys. Rev. A

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• Entanglement of two distant Bose-Einstein condensates by detection of Bragg-scattered photons
• Separability of a family of one parameter W and GHZ multiqubit states using Abe-Rajagopal q-conditional entropy approach
• Characterizing nonlocality of pure symmetric three-qubit states
• Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems
• A scheme for amplification and discrimination of photons