  We theoretically study the conditional counting statistics of electron
transport through a system consisting of a single quantum dot (SQD) or
coherently coupled double quantum dots (DQD's) monitored by a nearby quantum
point contact (QPC) using the generating functional approach with the maximum
eigenvalue of the evolution equation matrix method, the quantum trajectory
theory method (Monte Carlo method), and an efficient method we develop. The
conditional current cumulants that are significantly different from their
unconditional counterparts can provide additional information and insight into
the electron transport properties of mesoscopic nanostructure systems. The
efficient method we develop for calculating the conditional counting statistics
is numerically stable, and is capable of calculating the conditional counting
statistics for a more complex system than the maximum eigenvalue method and for
a wider range of parameters than the quantum trajectory method. We apply our
method to investigate how the QPC shot noise affects the conditional counting
statistics of the SQD system, going beyond the treatment and parameter regime
studied in the literature. We also investigate the case when the interdot
coherent coupling is comparable to the dephasing rate caused by the back action
of the QPC in the DQD system, in which there is considerable discrepancy in the
calculated conditional current cumulants between the population rate (master-)
equation approach of sequential tunneling and the full quantum master-equation
approach of coherent tunneling.
