Projective measurements can probe non-classical work extraction and time-correlations

We demonstrate an experimental technique to characterize genuinely nonclassical multi-time correlations using projective measurements with no ancillae. We implement the scheme in a nitrogen-vacancy center in diamond undergoing a unitary quantum work protocol. We reconstruct quantum-mechanical time correlations encoded in the Margenau-Hills quasiprobabilities. We observe work extraction peaks five times those of sequential projective energy measurement schemes and in violation of newly-derived stochastic bounds. We interpret the phenomenon via anomalous energy exchanges due to the underlying negativity of the quasiprobability distribution.