Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices

Abstract

We show that higher order inter-group covariances involving even number of qubits are necessarily positive semidefinite for N qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order inter-group covariance matrices of symmetric N-qubit systems. These conditions have a simple structure and detect entanglement in all even partitions of the symmetric multiqubit system. The observables involved are feasible experimental quantities and do not demand full state determination through quantum state tomography.

4 pages, no figures, RevTeX, Improved presentation

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• Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage
• Multipartite Entanglement Criterion from Uncertainty Relations
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• Entanglement of two distant Bose-Einstein condensates by detection of Bragg-scattered photons
• Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics
• Separability bounds on multiqubit moments due to positivity under partial transpose