Entanglement in continuous variable systems: Recent advances and current perspectives

Abstract

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, and its consequences for the characterization of 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.

61 pages, 7 figures, 3 tables; Published as Topical Review in J. Phys. A, Special Issue on Quantum Information, Communication, Computation and Cryptography (v3: few typos corrected)

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Cited by in corpus (13)

• Entanglement detection
• Continuous variable entanglement sharing in non-inertial frames
• Multi-mode bosonic Gaussian channels
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• Quantum Benchmark for Teleportation and Storage of Squeezed States
• Genuine multipartite entanglement of symmmetric Gaussian states: Strong monogamy, unitary localization, scaling behavior, and molecular sharing structure
• Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States
• Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
• Multipartite Continuous Variable Solution for the Byzantine Agreement Problem
• Coexistence of unlimited bipartite and genuine multipartite entanglement: Promiscuous quantum correlations arising from discrete to continuous variable systems
• Experimentally friendly bounds on non-Gaussian entanglement from second moments
• Operational Quantification of Continuous Variable Correlations
• Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations