# Feynman graphs and the large dimensional limit of multipartite entanglement. (arXiv:1702.04919v1 [math-ph])

We are interested in the properties of multipartite entanglement of a system

composed by $n$ $d$-level parties (qudits).

Focussing our attention on pure states we want to tackle the problem of the

maximization of the entanglement for such systems. In particular we effort the

problem trying to minimize the purity of the system. It has been shown that not

for all systems this function can reach its lower bound, however it can be

proved that for all values of $n$ a $d$ can always be found such that the lower

bound can be reached.

In this paper we examine the high-temperature expansion of the distribution

function of the bipartite purity over all balanced bipartition considering its

optimization problem as a problem of statistical mechanics. In particular we

prove that the series characterizing the expansion converges and we analyze the

behavior of each term of the series as $d\to \infty$.