We theoretically study the conditional counting statistics of electrontransport through a system consisting of a single quantum dot (SQD) orcoherently coupled double quantum dots (DQD's) monitored by a nearby quantumpoint contact (QPC) using the generating functional approach with the maximumeigenvalue of the evolution equation matrix method, the quantum trajectorytheory method (Monte Carlo method), and an efficient method we develop. Theconditional current cumulants that are significantly different from theirunconditional counterparts can provide additional information and insight intothe electron transport properties of mesoscopic nanostructure systems. Theefficient method we develop for calculating the conditional counting statisticsis numerically stable, and is capable of calculating the conditional countingstatistics for a more complex system than the maximum eigenvalue method and fora wider range of parameters than the quantum trajectory method. We apply ourmethod to investigate how the QPC shot noise affects the conditional countingstatistics of the SQD system, going beyond the treatment and parameter regimestudied in the literature. We also investigate the case when the interdotcoherent coupling is comparable to the dephasing rate caused by the back actionof the QPC in the DQD system, in which there is considerable discrepancy in thecalculated conditional current cumulants between the population rate (master-)equation approach of sequential tunneling and the full quantum master-equationapproach of coherent tunneling.
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