具有最大Schmidt测度的二可着色图态
Two-colorable graph states with maximal Schmidt measure
摘要：
Schmidt测度由Schmidt和Briegel引入，用于量化多体量子系统的纠缠度[Phys. Rev. A 64，022306（2001）]。虽然通常难以处理，但事实证明，对于两个可着色图状态，施密特测度存在一个界限[Phys. Rev. A 69，062311（2004）]。对于这些状态，施密特测度实际上与关联图的邻接矩阵的非零特征值的数量直接相关。我们注意到，几乎所有的两个着色图状态有最大施密特测度，我们构造具体的例子。这些涉及完美树，线图的树，cographs，图从反阿达玛矩阵，和unyciclic图。考虑了一些图的变换，其思想是把一个具有最大Schmidt测度的二色图态变换成另一个具有同样性质的二色图态。特别是，我们认为介绍了弗朗索瓦耶格，线图和开关的转换。借助Escherichfeucht等人[Discrete Math.278（2004）]的一个结果，我们指出局部互补和交换形成作用于给定维数的所有图状态的集合上的传递群。
英文摘要：
The Schmidt measure was introduced by Eisert and Briegel for quantifying the degree of entanglement of multipartite quantum systems [Phys. Rev. A 64, 022306 (2001)]. Although generally intractable, it turns out that there is a bound on the Schmidt measure for two-colorable graph states [Phys. Rev. A 69, 062311 (2004)]. For these states, the Schmidt measure is in fact directly related to the number of nonzero eigenvalues of the adjacency matrix of the associated graph. We remark that almost all two-colorable graph states have maximal Schmidt measure and we construct specific examples. These involve perfect trees, line graphs of trees, cographs, graphs from anti-Hadamard matrices, and unyciclic graphs. We consider some graph transformations, with the idea of transforming a two-colorable graph state with maximal Schmidt measure into another one with the same property. In particular, we consider a transformation introduced by Francois Jaeger, line graphs, and switching. By making appeal to a result of Ehrenfeucht et al. [Discrete Math. 278 (2004)], we point out that local complementation and switching form a transitive group acting on the set of all graph states of a given dimension.
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