Statistical mechanics of multipartite entanglement in hypergraph states
Abstract
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 2n 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 ≤ 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.
Related
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BibTeX
@misc{scarafile2026statistical,
title = {{Statistical mechanics of multipartite entanglement in hypergraph states}},
author = {Paolo Scarafile and Giorgia Trotta and Paolo Facchi and Giuseppe Magnifico and Giorgio Parisi and Saverio Pascazio and Karol Życzkowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24508},
eprint = {2609.24508},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24508},
}
RIS
TY - UNPB
TI - Statistical mechanics of multipartite entanglement in hypergraph states
AU - Paolo Scarafile
AU - Giorgia Trotta
AU - Paolo Facchi
AU - Giuseppe Magnifico
AU - Giorgio Parisi
AU - Saverio Pascazio
AU - Karol Życzkowski
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.24508
UR - https://arxiv.org/abs/2609.24508
AB - 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 ≤ 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.
ER -