On the problem of negative probabilities in time-resolved full counting statistics

We show that the standard Keldysh formulation of full counting statistics breaks down, when trying to interpret it directly in terms of a probability for time-dependent currents, since it leads to negative probability density. We propose a positive operator valued measure, which effectively accounts for some detector dynamics, but reproduces the Keldysh result in the low-frequency limit. However, the detector dynamics adds a large white Gaussian detection noise, which should be visible in experiment. The original negative probability can be measured indirectly by two independent detectors.