A preprint posted to arXiv — not yet peer-reviewed — proposes a statistical-mechanics framework for characterizing multipartite entanglement in hypergraph states, a structured family of pure n-qubit states. The authors map average bipartite purity onto an effective Hamiltonian of 2n classical binary spins, with each hypergraph state corresponding to a distinct spin configuration. In this analogy, temperature interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature, with the zero-temperature entropy's exponential yielding, the authors claim, the count of MMES within the hypergraph family.
For systems up to five qubits the team performs exact enumeration, fully characterizing the energy landscape and recovering previously known MMES counts. For n = 6 and 7, where exact methods are computationally prohibitive, they deploy simulated annealing and parallel tempering to sample the exponentially large state space. The algorithms produce quantitative predictions of MMES abundance and reveal how entanglement is distributed statistically across the full set of hypergraph states at finite temperature.
The authors argue that the thermodynamic mapping establishes hypergraph states as a tractable platform for studying multipartite entanglement structure, providing both concrete computational tools and conceptual insight into how entanglement organizes itself within restricted families of quantum states. As an unreviewed preprint, the results — including the predicted MMES counts for larger system sizes — await independent validation before they can be considered established.