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We show that entanglement monotones can characterize the pronouncedenhancement of entanglement at a quantum phase transition if they are sensitiveto long-range high order correlations. These monotones are found to develop asharp peak at the critical point and to exhibit universal scaling. Wedemonstrate that similar features are shared by noise correlations and verifythat these experimentally accessible quantities indeed encode entanglementinformation and probe separability.

Phase transitions, entanglement and quantum noise interferometry in cold atoms