Continuous variable tangle and entanglement sharing of Gaussian states

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  • 23 June 2005
Abstract
We introduce an infinite-dimensional generalization of the tangle (the {\em contangle}) that quantifies the distributed entanglement of multimode Gaussian states. We prove that it satisfies the continuous-variable version of the Coffman-Kundu-Wootters monogamy inequality in all three--mode, and in fully symmetric $N$--mode Gaussian states. The resulting residual contangle is proven to be a tripartite entanglement monotone under Gaussian LOCC. We show that pure, symmetric three--mode Gaussian states allow a promiscuous sharing of quantum correlations, exhibiting both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes.

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