2004/10/31 by Gerardo Adesso, Fabrizio Illuminati · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #cond-mat.other #math-ph #math.MP #physics.optics #quant-ph
paper · pdf · doi:10.1088/1367-2630/8/1/015
published as New J. Phys. 8, 15 (2006) · 13 pages, 1 figure. Replaced with published version
openalex publication_date 2006/01/30 · arxiv created 2006/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
For continuous-variable systems, we introduce a measure of entanglement, the continuous variable tangle (\em contangle), with the purpose of quantifying the distributed (shared) entanglement in multimode, multipartite Gaussian states. This is achieved by a proper convex roof extension of the squared logarithmic negativity. We prove that the contangle satisfies the Coffman-Kundu-Wootters monogamy inequality in all three--mode Gaussian states, and in all fully symmetric N--mode Gaussian states, for arbitrary N. For three--mode pure states we prove that the residual entanglement is a genuine tripartite entanglement monotone under Gaussian local operations and classical communication. We show that pure, symmetric three--mode Gaussian states allow a promiscuous entanglement sharing, having both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. These states are thus simultaneous continuous-variable analogs of both the GHZ and the W states of three qubits: in continuous-variable systems monogamy does not prevent promiscuity, and the inequivalence between different classes of maximally entangled states, holding for systems of three or more qubits, is removed.