叠加缠结与凸顶延伸
Tangles of superpositions and the convex-roof extension
摘要：
我们讨论了凸屋顶扩展的多体纠缠措施，即$SL(2,\CC)$不变缠结方面。我们强调两个关键的概念，包含有价值的信息的纠缠的密度矩阵：{ \em零多面体}是一个凸集的密度矩阵消失的纠缠，而{ \em凸特征曲线}很容易提供一个非平凡的下界的凸屋顶，并作为一种工具，用于构建凸屋顶以外的零多面体。这两个概念都是从密度矩阵的本征态叠加的缠结中导出的。我们通过考虑秩为2的两量子比特和三量子比特状态的密度矩阵的例子来说明它们的应用，从而指出概念的能力和局限性。
英文摘要：
We discuss aspects of the convex-roof extension of multipartite entanglement measures, that is, $SL(2,\CC)$ invariant tangles. We highlight two key concepts that contain valuable information about the tangle of a density matrix: the {\em zero-polytope} is a convex set of density matrices with vanishing tangle whereas the {\em convex characteristic curve} readily provides a non-trivial lower bound for the convex roof and serves as a tool for constructing the convex roof outside the zero-polytope. Both concepts are derived from the tangle for superpositions of the eigenstates of the density matrix. We illustrate their application by considering examples of density matrices for two-qubit and three-qubit states of rank 2, thereby pointing out both the power and the limitations of the concepts.
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