General large-N behavior of the Q-family

Determine the large-$N$ behavior of $Q_{m,n,p,q}^{(c)}$ in Haar-random states for arbitrary positive integers $m,n,p,q$, beyond the explicitly evaluated case $Q_{0,0,0,0}^{(c)}$.

Background

The paper obtains an explicit leading-order estimate for the special spread Q0,0,0,0(c)Q_{0,0,0,0}^{(c)}. For general positive parameters, it establishes only upper bounds on the degrees of compatibility of the graphs defining the spread.

Those bounds alone do not determine the large-NN asymptotics. The authors therefore leave the general asymptotic evaluation unresolved.

References

This observation is not by itself sufficient to determine the large-$N$ behaviour of $Q_{m,n,p,q}{(c)}({\varphi_N})$ for arbitrary values of $m,n,p,q$, we therefore leave this question open for the future.

— Multipartite entanglement spreads  (2610.12271 - Carrozza et al., 8 Oct 2026) in End of Section 3.2 (Second family: minimizers obey equations enabling the elimination of non-separating 1-dipoles)