Interferometry of quantum correlation functions to access quasiprobability distribution of work

The Kirkwood-Dirac quasiprobability distribution, intimately connected with the quantum correlation function of two observables measured at distinct times, is becoming increasingly relevant for fundamental physics and quantum technologies. This quasiprobability distribution can take non-positive values, and its experimental reconstruction becomes challenging when expectation values of incompatible observables are involved. Here, we use an interferometric scheme aided by an auxiliary system to reconstruct the Kirkwood-Dirac quasiprobability distribution. We experimentally demonstrate this scheme in an electron-nuclear spin system associated with a nitrogen-vacancy center in diamond. By measuring the characteristic function, we reconstruct the quasiprobability distribution of work and analyze the behavior of its first and second moments. Our results clarify the physical meaning of the work quasiprobability distribution in the context of quantum thermodynamics. Finally, we study the uncertainty of measuring the Hamiltonian of the system at two times, via the Robertson-Schr{ö}dinger uncertainty relation, for different initial states.