Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
Continuous variable tangle, monogamy inequality, and entanglement sharing in Gaussian states of continuous variable systems
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DOI：
10.1088/1367-2630/8/1/015
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发表时间：
2004-10
影响因子：
3.3
通讯作者：
G. Adesso;F. Illuminati
中科院分区：
文献类型：
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作者：
G. Adesso;F. Illuminati
对于连续变量（CV）系统，我们引入了一种纠缠度量，CV缠结（conangle），目的是量化多模多体高斯态中的分布式（共享）纠缠。这是通过适当的凸屋顶扩展的平方对数负。我们证明了在所有三模高斯态和所有完全对称的N模高斯态中，对于任意的N，纠缠角满足Coffman-Kundu-Wootters一夫一妻不等式。对于三模纯态，我们证明了在高斯局域操作和经典通信下，剩余纠缠是真正的三重纠缠单调。我们发现，纯的，对称的三模高斯态允许混杂的纠缠共享，具有最大的三方剩余纠缠和最大的耦合纠缠之间的任何一对模式。因此，这些状态是三个量子比特的GHZ和W状态的同时CV类似物：在CV系统中，一夫一妻制并不能防止滥交，并且消除了不同类别的最大纠缠态之间的不等价性，适用于三个或更多量子比特的系统。
For continuous-variable (CV) systems, we introduce a measure of entanglement, the CV tangle (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 CV analogues of both the GHZ and the W states of three qubits: in CV 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.