多进制量子图态纠缠的确定

Determing the entanglement of quantum nonbinary graph states

图态是可以与数学上的图对应起来的多组分纠缠态,图的顶点在此扮演多进制量子位而连线则表示两个多进制量子位之间的相互作用.图态在量子纠错码、多体量子计算和单向量子计算中起重要作用.本文系统研究多进制图态纠缠,使用迭代计算等方法计算了局域幺正变换和图同构下不等价的所有9点图以下的三进制图态的纠缠及一部分四进制和五进制图态的纠缠,纠缠测度可以是几何纠缠、相对熵纠缠和鲁棒性纠缠.我们对计算结果进行了分类,并分析了所得到的最近分离态.

Graph states are multipartite entangled states that correspond to mathematical graphs, where the vertices of the graph now play the role of quantum multilevel systems and edges represent interactions of the systems. Graph states are the basis of quantum error correction and one-way quantum computer. We systematically study the entanglement of non-binary graph states. Using iterative algorithm and entanglement bounds, we calculate the entanglement of all the ternary graph states up to nine vertices and parts of quaternary and quinary graph states modulo local unitary transformations and graph isomorphisms. The entanglement measure can be the geometric measure, the measure of relative entropy of entanglement or the measure of logarithmic robustness. We classify the graph states according to the entanglement values obtained. The closest product states obtained in the calculations are studied.