发表机构
Università di Napoli; INFN, Sezione di Bari; Università di Bari; Università degli Studi di Roma La Sapienza; Istituto Nazionale di Fisica Nucleare, Sezione di Roma I; Institute of Nanotechnology (NANOTEC) - CNR, Rome unit; Jagiellonian University; Center for Theoretical Physics (CFT), Polish Academy of Sciences（那不勒斯大学; 意大利国家核物理研究所巴里分部; 巴里大学; 罗马第一大学; 意大利国家核物理研究所罗马一分部; 纳米技术研究所（NANOTEC）- 国家研究委员会罗马分部; 雅盖隆大学; 波兰科学院理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用统计力学框架研究超图态的多体纠缠，通过温度插值联系随机态与最大纠缠态，并用精确枚举和采样算法预测MMES数量，揭示纠缠统计分布。
AI 中文摘要
我们通过统计力学框架研究了一类纯$n$量子比特超图态中的多体纠缠，其中平均二分纯度映射到$2^n$个经典二值自旋的有效哈密顿量上。在这种对应关系中，每个超图态唯一对应一个经典自旋构型，而温度作为控制参数，在高温下的随机超图态均匀系综与零温度下的最大多体纠缠态（MMES）之间连续插值。值得注意的是，零温度熵的指数直接给出了超图态集合中MMES的数量。对于小系统尺寸（$n \leq 5$），我们进行了精确枚举，全面刻画了能量景观和相关的热力学观测量，并验证了已知的MMES计数。对于较大系统（$n = 6$和$7$），精确方法在计算上变得不可行，我们采用模拟退火和并行回火算法来高效采样指数级大的状态空间。我们的分析得出了MMES数量的定量预测，并揭示了纠缠在超图态集合中的统计分布。这些结果确立了超图态作为通过热力学方法研究多体纠缠的理想平台，为受限量子态族中量子纠缠的结构提供了计算进展和物理见解。
英文摘要
We investigate multipartite entanglement in a particular family of pure $n$-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of $2^n$ classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes ($n \leq 5$), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems ($n = 6$ and $7$), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.
Comments14 pages, 6 figures
