论文标题
图形状态的张量排名和其他多部分纠缠度量
Tensor Rank and Other Multipartite Entanglement Measures of Graph States
论文作者
论文摘要
图状态通过与基于测量的计算和误差校正的联系在量子信息理论中起重要作用。先前的工作揭示了这些状态的图形结构与其多部分纠缠内容之间的优雅连接。我们通过确定某些类型的图形状态的其他纠缠属性来继续进行这一调查。从张量理论的角度来看，我们在奇数环状态（$ | r_ {2n+1} \ rangle $）上拧紧上限和下限，以读取$ 2^n+1 \ leq stark（| r_ {2n+1} \ rangle）接下来，我们表明，基于相应图的连通性，两部分纠缠措施的多个多部分扩展是二分法的。最后，我们给出了一个简单的图形规则，用于计算n-tangle $τ_n$。
Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and their multipartite entanglement content. We continue this line of investigation by identifying additional entanglement properties for certain types of graph states. From the perspective of tensor theory, we tighten both upper and lower bounds on the tensor rank of odd ring states ($|R_{2n+1}\rangle$) to read $2^n+1 \leq rank(|R_{2n+1}\rangle) \leq 3*2^{n-1}$. Next, we show that several multipartite extensions of bipartite entanglement measures are dichotomous for graph states based on the connectivity of the corresponding graph. Lastly, we give a simple graph rule for computing the n-tangle $τ_n$.
