Negative Full Counting Statistics Arise From Interference Effects

The Keldysh-ordered full counting statistics is a quasi-probability distribution describing the fluctuations of a time-integrated quantum observable. While it is well known that this distribution can fail to be positive, the interpretation and origin of this negativity has been somewhat unclear. Here, we show how the full counting statistics can be tied to trajectories through Hilbert space, and how this directly connects negative quasi-probabilities to an unusual interference effect. Our findings are illustrated with the example of energy fluctuations in a driven bosonic resonator; we discuss how negative quasi-probability here could be detected experimentally using superconducting microwave circuits.