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 $d\to \infty$.