Conditional statistics of electron transport in interacting mesoscopic devices

The conditional operationa and dynamics has been one of the focused topics in the field of quantum information processing. We present here a theoretical study of the conditional counting statistics for interacting mesoscopic electronic devices. The conditional counting statistics that is the statistical current fluctuations of one system given the observation of a particular current in the other system could be substantially different from their unconditional counterpart. Based on the number-resolved quantum master equation approach and the full counting statistics method, we calculate the conditional statistics of current cumulants in a coupled quantum dot system in parallel. We also discuss the underlying electron transport corresponding to different external gate voltage regimes of the two-coupled quantum dot system. We find the conditional statistics can help better understand the system's properties as it provides more information than the usual unconditional statistical quantities.