  A bipartite quantum system in a mixed state can exhibit nonclassical
correlations, which can go beyond quantum entanglement. While quantum discord
is the standard measure of quantifying such general quantum correlations, the
nonclassicality can be determined by simpler means via the measurement of
witness operators. We experimentally construct a positive map to witness
nonclassicality of two qubits in an NMR system. The map can be decomposed so
that a single run of an experiment on an ensemble of spins suffices to detect
the nonclassicality in the state, if present. We let the state evolve in time
and use the map to detect nonclassicality as a function of time. To evaluate
the efficacy of the witness operator as a means to detect nonclassicality, we
measure quantum discord by performing full quantum state tomography at each
time point and obtained a fairly good match between the two methods.
