Projective measurements can probe nonclassical work extraction and time correlations

Quantum correlation functions are a natural way to encode multitime information, as they are ubiquitous in analysis from fluctuation theorems to information scrambling. Correlation functions can be identified with quasiprobabilities associated to quantum processes. In this work we show how these can be measured via error-cancellation techniques, using projective measurements only and no ancillae. The scheme is implemented 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 by observing 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.