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Recent work has revealed the central role played by the Kirkwood-Diracquasiprobability (KDQ) as a tool to properly account for non-classical featuresin the context of condensed matter physics (scrambling, dynamical phasetransitions) metrology (standard and post-selected), thermodynamics (poweroutput and fluctuation theorems), foundations (contextuality, anomalous weakvalues) and more. Given the growing relevance of the KDQ across the quantumsciences, our aim is two-fold: First, we highlight the role played byquasiprobabilities in characterizing the statistics of quantum observables andprocesses in the presence of measurement incompatibility. In this way, we showhow the KDQ naturally underpins and unifies quantum correlators, quantumcurrents, Loschmidt echoes, and weak values. Second, we provide noveltheoretical and experimental perspectives by discussing a wide variety ofschemes to access the KDQ and its non-classicality features.

Kirkwood-Dirac quasiprobability approach to the statistics of incompatible observables