Geometric characterization of separability and entanglement in pure Gaussian states by single-mode unitary operations

Gerardo Adesso, Salvatore M. Giampaolo, Fabrizio Illuminati

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    8 Citations (Scopus)

    Abstract

    We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single subsystem unitary transformations that has been recently introduced to characterize separability and entanglement in pure states of qubits and qutrits. In analogy with the finite-dimensional case, we demonstrate that the 1 M bipartite entanglement of a multimode pure Gaussian state can be quantified by the minimum squared Euclidean distance between the state itself and the set of states obtained by transforming it via suitable local symplectic (unitary) operations. This minimum distance, corresponding to a, uniquely determined, extremal local operation, defines an entanglement monotone equivalent to the entropy of entanglement, and amenable to direct experimental measurement with linear optical schemes. © 2007 The American Physical Society.
    Original languageEnglish
    Article number042334
    JournalPhysical Review A - Atomic, Molecular, and Optical Physics
    Volume76
    Issue number4
    DOIs
    Publication statusPublished - 26 Oct 2007

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