  We investigate the usage of a recently introduced noise-cancellation
algorithm for Brownian simulations to enhance the precision of measuring
transport properties such as the mean-square displacement or the
velocity-autocorrelation function. The algorithm is based on explicitly storing
the pseudo-random numbers used to create the randomized displacements in
computer simulations and subtracting them from the simulated trajectories. The
resulting correlation function of the reduced motion is connected to the target
correlation function up to a cross-correlation term. Using analytical theory
and computer simulations, we demonstrate that the cross-correlation term can be
neglected in all three systems studied in this aper. We further expand the
algorithm to Monte Carlo simulations and analyze the performance of the
algorithm and rationalize that it works particularly well for unbounded, weakly
interacting systems in which the precision of the mean-square displacement can
be improved by orders of magnitude.
