Kirkwood-Dirac quasiprobability approach to quantum fluctuations: Theoretical and experimental perspectives

Recent work has revealed the central role played by the Kirkwood-Dirac quasiprobability (KDQ) as a tool to encapsulate non-classical features in the context of condensed matter physics (scrambling, dynamical phase transitions) metrology (standard and post-selected), thermodynamics (power output and fluctuation theorems), foundations (contextuality, anomalous weak values) and more. Given the growing relevance of the KDQ across the quantum sciences, the aim of this work is two-fold: first, we clarify the role played by quasiprobabilities in characterising dynamical fluctuations in the presence of measurement incompatibility, and highlight how the KDQ naturally underpins and unifies quantum correlators, quantum currents, Loschmidt echoes and weak values; second, we discuss several schemes to access the KDQ and its non-classicality features, and assess their experimental feasibility in NMR and solid-state platforms. Finally, we analyze the possibility of a `thermodynamics with quasiprobabilities' in the light of recent no-go theorems limiting traditional treatments.