  Consider a two-party correlation that can be generated by performing local
measurements on a bipartite quantum system. A question of fundamental
importance is to understand how many resources, which we quantify by the
dimension of the underlying quantum system, are needed to reproduce this
correlation. In this Letter, we identify an easy-to-compute lower bound on the
smallest Hilbert space dimension needed to generate a given two-party quantum
correlation. We show that our bound is tight on many well-known correlations
and discuss how it can rule out correlations of having a finite-dimensional
quantum representation. We show that our bound is multiplicative under product
correlations and also that it can witness the non-convexity of certain
restricted-dimensional quantum correlations.
