Quantum advantage from negativity of work quasiprobability distributions

Quantum batteries can be charged by performing a work “instantaneously” in the limit of a large number of cells, achieving a so-called quantum advantage. In general, the work exhibits statistics that can be represented by a quasiprobability in the presence of initial quantum coherence in the energy basis. Here, we show that these two concepts of quantum thermodynamics, which apparently appear disconnected, can show a simple relation. Specifically, if a certain work distribution shows negativity asymptotically in the limit of a large number of cells and in a certain time interval, then we surely get a quantum advantage in the charging process. In particular, we prove this for a direct charging protocol performed with a class of charging Hamiltonian operators.