© 2018 Author(s). In this paper, we extend the analysis of multipartite entanglement, based on techniques from classical statistical mechanics, to a system composed of n d-level parties (qudits). We introduce a suitable partition function at a fictitious temperature with the average local purity of the system as Hamiltonian. In particular, we analyze the high-temperature expansion of this partition function, prove the convergence of the series, and study its asymptotic behavior as d → ∞. We make use of a diagrammatic technique, classify the graphs, and study their degeneracy. We are thus able to evaluate their contributions and estimate the moments of the distribution of the local purity.
Di Martino, S., Facchi, P., & Florio, G. (2018). Feynman graphs and the large dimensional limit of multipartite entanglement. Journal of Mathematical Physics, 59(1), . https://doi.org/10.1063/1.5019481