  Bipartite correlations generated by non-signalling physical systems that
admit a finite-dimensional local quantum description cannot exceed the quantum
limits, i.e., they can always be interpreted as distant measurements of a
bipartite quantum state. Here we consider the effect of dropping the assumption
of finite dimensionality. Remarkably, we find that the same result holds
provided that we relax the tensor structure of space-like separated
measurements to mere commutativity. We argue why an extension of this result to
tensor representations seems unlikely.
