A family of many-body quantum states is said to satisfy an "area law" if the entanglement between a region A and its complement B scales only as the size of the boundary between them. We intuitively expect this for states that are in some sense "local," and/or produced by local Hamiltonians. However, rigorous results in this direction are quite involved and generally restricted to 1D chains with short-range correlations. Here we present joint work (in progress) with Fernando Brandao on a new proof technique that may yield area laws--albeit in a weaker dynamical form--in higher dimensions and for longer-range interactions. This technique proceeds by measuring sites of B one-by-one, and evaluating their correlations with A conditioned on the outcomes.