  We analyze the effects of quantum correlations, such as entanglement and
discord, on the efficiency of phase estimation by studying four quantum
circuits that can be readily implemented using NMR techniques. These circuits
define a standard strategy of repeated single-qubit measurements, a classical
strategy where only classical correlations are allowed, and two quantum
strategies where nonclassical correlations are allowed. In addition to counting
space (number of qubits) and time (number of gates) requirements, we introduce
mixedness as a key constraint of the experiment. We compare the efficiency of
the four strategies as a function of the mixedness parameter. We find that the
quantum strategy gives square-root of N enhancement over the standard strategy
for the same amount of mixedness. This result applies even for highly mixed
states that have nonclassical correlations but no entanglement.
