Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics

The probabilistic nature of quantum measurements is central to the deep philosophical questions regarding the foundations of quantum mechanics. It is also of great practical importance, since experimenters can only observe quantum systems indirectly through these measurements. One particularly important scenario is that of continuous measurements, where information about the system is available in the form of an output current, a classical time series which is fundamentally stochastic in nature. The theory of continous quantum measurements is very mature, particulary from the perspective of quantum optics. On the other hand, condensed matter physicists, often use full counting statistics and scattering theory to describe counting measurements, and their statistics using the cumulant generating function. In this talk, I will show how these two concepts can be bridged such that both frameworks can be leveraged simultaneously to better study, and compute, the statistical properties of quantum measurements.