Coauthors: C. A. Ryan, D. G. Cory, R. Laflamme

We present a protocol to estimate the expectation value of the correlations of measurement outcomes for ensembles of quantum systems, and use it to experimentally demonstrate-under an assumption of fair sampling-the violation of an inequality that is satisfied by any non-contextual hidden-variables theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established Nuclear Magnetic Resonance (NMR) techniques for quantum information processing.