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arXiv 2209.06320quant-phmath-phmath.MP
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图态的张量秩及其他多体纠缠度量

Tensor Rank and Other Multipartite Entanglement Measures of Graph States

Louis Schatzki, Linjian Ma, Edgar Solomonik, Eric Chitambar

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9 + 5 pages, 5 figures
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AI总结：

本文研究图态的多体纠缠性质，收紧奇环态张量秩的上下界，证明若干多体纠缠度量对图态具有基于图连通性的二分特性，并给出计算 n-tangle 的简单图规则。

摘要：

图态通过其与基于测量的计算和纠错的联系，在量子信息理论中发挥着重要作用。先前的工作揭示了这些态的图结构与其多体纠缠内容之间的优美联系。我们继续这一研究方向，为某些类型的图态识别出额外的纠缠性质。从张量理论的角度，我们将奇环态（$|R_{2n+1}\rangle$）的张量秩上下界收紧为 $2^n+1 \leq rank(|R_{2n+1}\rangle) \leq 3*2^{n-1}$。接下来，我们证明，基于相应图的连通性，二体纠缠度量的若干多体推广对于图态是二分的。最后，我们给出一个用于计算 n-tangle $τ_n$ 的简单图规则。

英文摘要：

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 $τ_n$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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