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

Abstract

Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e. simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N >= 4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding is of importance for the quantification, understanding and potential exploitation of shared quantum correlations in continuous variable systems. We discuss how promiscuity gradually 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 asymptotically diverging, but finite squeezing. In this respect, we find that non-Gaussian states (which in general are more entangled than Gaussian states), exhibit also the interesting feature that their entanglement is more shareable: in the non-Gaussian multipartite arena, unlimited promiscuity can be already achieved among three entangled parties, while this is impossible for Gaussian, even infinitely squeezed states.

8 pages, 4 figures. Extended version. Added discussion about entanglement sharing and its promiscuous structure in qudits and non-Gaussian states

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• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• A Quantum Information Perspective on Many-Body Dispersive Forces
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels
• Noisy dynamics of Gaussian entanglement: a transient bound entangled phase before separability