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Quantum mechanics imposes 'monogamy' constraints on the sharing ofentanglement. We show that, despite these limitations, entanglement can befully 'promiscuous', i.e. simultaneously present in unlimited two-body andmany-body forms in states living in an infinite-dimensional Hilbert space.Monogamy just bounds the divergence rate of the various entanglementcontributions. This is demonstrated in simple families of N-mode (N >= 4)Gaussian states of light fields or atomic ensembles, which therefore enableinfinitely more freedom in the distribution of information, as opposed tosystems of individual qubits. Such a finding is of importance for thequantification, understanding and potential exploitation of shared quantumcorrelations in continuous variable systems. We discuss how promiscuitygradually arises when considering simple families of discrete variable states,with increasing Hilbert space dimension towards the continuous variable limit.Such models are somehow analogous to Gaussian states with asymptoticallydiverging, but finite squeezing. In this respect, we find that non-Gaussianstates (which in general are more entangled than Gaussian states), exhibit alsothe interesting feature that their entanglement is more shareable: in thenon-Gaussian multipartite arena, unlimited promiscuity can be already achievedamong three entangled parties, while this is impossible for Gaussian, eveninfinitely squeezed states.Comment: 8 pages, 4 figures. Extended version. Added discussion about  entanglement sharing and its promiscuous structure in qudits and non-Gaussian  state

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous-variable systems