  Recently, we introduced a solution to the quantum marginal problem relevant
to two-dimensional quantum many-body systems [I. H. Kim, Phys. Rev. X, 11,
021039]. One of the conditions was that the marginals are internally
translationally invariant. We show that this condition can be replaced by a
weaker condition, namely the local consistency of the marginals. This extends
the applicability of the solution to any quantum many-body states in two
dimensions that satisfy the entropy scaling law, with or without symmetry. We
also significantly simplify the proof by advocating the usage of the
maximum-entropy principle.
