Entanglement in continuous-variable systems: recent advances and current perspectives

By Gerardo Adesso, Fabrizio Illuminati. 2007

531 citations recorded by the source corpus.

We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states. Multipartite entanglement of Gaussian states is reviewed by discussing its qualification by different classes of separability, and the main consequences of the monogamy inequality, such as the quantification of genuine tripartite entanglement in three-mode Gaussian states, the promiscuous nature of entanglement sharing in symmetric Gaussian states and the possible coexistence of unlimited bipartite and multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non-Gaussian states, a field of research that is to a large extent yet to be explored.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1b3d34cad325f326bce3c91acab05482d09144e2

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Citations in the corpus

Quantum interface between light and atomic ensembles (2008, background): “A useful and comprehensive review of the theory of entanglement in systems of continuous variables was recently given by Adesso and Illuminati (2007), for a concise introduction to the basic facts on the same topic see Eisert and Plenio (2003).”
Entanglement certification from theory to experiment (2018, background): “These challenges already arise for finite-dimensional systems, which we focus on here, referring the interested reader to existing reviews on continuous-variable entanglement [30–35], for a discussion of the fascinating intricacies of infinite-dimensional systems.”
Entanglement in many-body systems (2007, background): “In this section we concentrate on the entanglement between distinct modes of harmonic oscillators (see (Adesso and Illuminati, 2007; Braunstein and van Loock, 2005) for recent reviews on the subject).”
The classical-quantum boundary for correlations: Discord and related measures (2011, background): “Such states ρAB are fully specified, up to local displacements, by covariance matrix γ with entries γkl = tr[ρAB(RkRl + RlRk)], where ~R = (xA, pA, xB , pB) is the vector of phase-space operators (Adesso and Illuminati, 2007).”
Gaussian quantum information (2011, methodology): “The logarithmic negativity of 1 M and N M bisymmetric Gaussian states was characterized by Adesso, Serafini, and Illuminati (2004) and Adesso and Illuminati (2007), respectively.”
Sufficient Conditions for Efficient Classical Simulation of Quantum Optics (2015, unknown): “transmissivity ffiffiffiffiffiffiffi ηBL p [39].”