Entanglement of random hypergraph states
Entanglement of random hypergraph states
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DOI：
10.1103/physreva.106.012410
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发表时间：
2021-10
影响因子：
2.9
通讯作者：
You Zhou;A. Hamma
中科院分区：
文献类型：
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作者：
You Zhou;A. Hamma
随机量子态和随机量子操作具有重要的理论意义和实用价值。在这项工作中，我们研究了随机超图态的纠缠特性，它通过将广义控制相位门应用于初始参考乘积态来推广图态的概念。特别地，我们分别研究了由随机控制Z（CZ）和控制-控制Z（CCZ）门产生的两个系综。利用张量网络表示和组合计数方法，分析表明两个系综的平均子系统纯度和纠缠熵具有相同的体积律，但典型性有很大不同，即CCZ系综的纯度起伏较小且具有普适性，而CZ系综的纯度起伏较大.我们讨论了纠缠复杂性和量子混沌的发病这些结果的影响。
Random quantum states and operations are of fundamental and practical interests. In this work, we investigate the entanglement properties of random hypergraph states, which generalize the notion of graph states by applying generalized controlled-phase gates on an initial reference product state. In particular, we study the two ensembles generated by random Controlled-Z(CZ) and Controlled-Controlled-Z(CCZ) gates, respectively. By applying tensor network representation and combinational counting, we analytically show that the average subsystem purity and entanglement entropy for the two ensembles feature the same volume law, but greatly differ in typicality, namely the purity fluctuation is small and universal for the CCZ ensemble while it is large for the CZ ensemble. We discuss the implications of these results for the onset of entanglement complexity and quantum chaos.