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

Gerardo Adesso, Marie Ericsson, Fabrizio Illuminati

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    11 Citations (Scopus)

    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. © 2007 The American Physical Society.
    Original languageEnglish
    Article number022315
    JournalPhysical Review A - Atomic, Molecular, and Optical Physics
    Volume76
    Issue number2
    DOIs
    Publication statusPublished - 15 Aug 2007

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