  Natural interactions among multiple quantum objects are fundamentally
composed of two-body terms only. In contradistinction, single global unitaries
that generate highly entangled states typically arise from Hamiltonians that
couple multiple individual subsystems simultaneously. Here, we study the time
to produce strongly nonclassical multipartite correlations with a single
unitary generated by the natural interactions. We restrict the symmetry of
two-body interactions to match the symmetry of the target states and focus on
the fastest generation of multipartite entangled Greenberger-Horne-Zeilinger
(GHZ), W, Dicke and absolutely maximally entangled (AME) states for up to seven
qubits. These results are obtained by constraining the energy in the system and
accordingly can be seen as state-dependent quantum speed limits for
symmetry-adjusted natural interactions. They give rise to a counter-intuitive
effect where the creation of particular entangled states with an increasing
number of particles does not require more time. The methods used rely on
extensive numerical simulations and analytical estimations.
