Quantum advantage from negativity of work quasiprobability distributions

Abstract: Quantum batteries can be charged by performing a work ``instantaneously'' if there is a large number of cells. 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, show a simple relation. Specifically, if the work distribution shows negativity in some time interval, then we can surely get quantum advantage in the charging process.