Testing Contextuality on Quantum Ensembles with One Clean Qubit

We present a protocol to evaluate 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 noncontextual hidden-variables theory. The experiment is performed on an ensemble of molecular nuclear spins in the solid state, using established nuclear magnetic resonance techniques for quantum-information processing.