  Constructing local hidden variable (LHV) models for entangled quantum states
is challenging, as the model should reproduce quantum predictions for all
possible local measurements. Here we present a simple method for building LHV
models, applicable to general entangled states, which consists in verifying
that the statistics resulting from a finite set of measurements is local, a
much simpler problem. This leads to a sequence of tests which, in the limit,
fully capture the set of quantum states admitting a LHV model. Similar methods
are developed for constructing local hidden state models. We illustrate the
practical relevance of these methods with several examples, and discuss further
applications.
