Monogamy inequality for distributed Gaussian entanglement

Abstract

We show that for all n-mode Gaussian states of continuous variable systems, the entanglement shared among n parties exhibits the fundamental monogamy property. The monogamy inequality is proven by introducing the Gaussian tangle, an entanglement monotone under Gaussian local operations and classical communication, which is defined in terms of the squared negativity in complete analogy with the case of n-qubit systems. Our results elucidate the structure of quantum correlations in many-body harmonic lattice systems.

4 pages, no figures. Several improvements, proof made more transparent, conclusions enriched

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• Continuous variable entanglement sharing in non-inertial frames
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• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• Monogamy and ground-state entanglement in highly connected systems
• Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations
• Entanglement sharing in $E\otimes \epsilon$ Jahn-Teller model in the presence of a magnetic field