Entanglement in continuous-variable systems: recent advances and current perspectives
Entanglement in continuous-variable systems: recent advances and current perspectives
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DOI：
10.1088/1751-8113/40/28/s01
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发表时间：
2007-07-13
影响因子：
2.1
通讯作者：
Illuminati, Fabrizio
中科院分区：
文献类型：
--
作者：
Adesso, Gerardo;Illuminati, Fabrizio
我们回顾了连续变量纠缠的理论，特别强调的基础方面，概念结构和数学方法。大量的注意力被用于讨论高斯态的可分性准则和纠缠特性，因为它们在量子光学和量子信息的应用中具有很大的实际意义，以及它们允许研究非局域关联结构的非常清晰的框架。我们给出了一个自足的介绍相空间和辛方法在研究无限维玻色子系统的高斯态。本文回顾了高斯态的可分性和可分离性的最重要结果，并讨论了两体纠缠的主要性质。其中包括双模混合高斯态的最大和最小极值纠缠，双模高斯态根据不同纠缠度量的排序，单模高斯态的幺正（可逆）局域化和两体纠缠的标度。然后讨论了多模高斯态纠缠共享的最新进展，包括高斯态分布式纠缠一夫一妻不等式的证明。讨论了高斯态的多体纠缠，讨论了不同类可分性对多体纠缠的限制，以及单偶不等式的主要结果，如三模高斯态中真正的三体纠缠的量化，对称高斯态中纠缠共享的混杂性质，无限二体纠缠和多体纠缠共存的可能性.最后，我们回顾了最近的进展，并讨论了在非高斯态，一个研究领域，在很大程度上还有待探索的纠缠的定性和定量的可能前景。
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.