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

Abstract

We review the theory of continuous-variable entanglement with special\nemphasis on foundational aspects, conceptual structures, and mathematical\nmethods. Much attention is devoted to the discussion of separability criteria\nand entanglement properties of Gaussian states, for their great practical\nrelevance in applications to quantum optics and quantum information, as well as\nfor the very clean framework that they allow for the study of the structure of\nnonlocal correlations. We give a self-contained introduction to phase-space and\nsymplectic methods in the study of Gaussian states of infinite-dimensional\nbosonic systems. We review the most important results on the separability and\ndistillability of Gaussian states and discuss the main properties of bipartite\nentanglement. These include the extremal entanglement, minimal and maximal, of\ntwo-mode mixed Gaussian states, the ordering of two-mode Gaussian states\naccording to different measures of entanglement, the unitary (reversible)\nlocalization, and the scaling of bipartite entanglement in multimode Gaussian\nstates. We then discuss recent advances in the understanding of entanglement\nsharing in multimode Gaussian states, including the proof of the monogamy\ninequality of distributed entanglement for all Gaussian states, and its\nconsequences for the characterization of multipartite entanglement. We finally\nreview recent advances and discuss possible perspectives on the qualification\nand quantification of entanglement in non Gaussian states, a field of research\nthat is to a large extent yet to be explored.\n

Keywords

Affiliated Institutions

• University of Salerno IT
• Istituto Nazionale di Fisica Nucleare, Sezione di Napoli IT
• Institute for Scientific Interchange IT
• Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Salerno
• Sapienza University of Rome IT

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