  Recent achievements in quantum control have resulted in advanced techniques
for designing controllers for applications in quantum communication, computing,
and sensing. However, the susceptibility of such systems to noise and
uncertainties necessitates robust controllers that perform effectively under
these conditions to realize the full potential of quantum devices. The
time-domain log-sensitivity and a recently introduced robustness infidelity
measure (RIM) are two means to quantify controller robustness in quantum
systems. The former can be found analytically, while the latter requires
Monte-Carlo sampling. In this work, the correlation between the log-sensitivity
and the RIM for evaluating the robustness of single excitation transfer
fidelity in spin chains and rings in the presence of dephasing is investigated.
We show that the expected differential sensitivity of the error agrees with the
differential sensitivity of the RIM, where the expectation is over the error
probability distribution. Statistical analysis also demonstrates that the
log-sensitivity and the RIM are linked via the differential sensitivity, and
that the differential sensitivity and RIM are highly concordant. This
unification of two means (one analytic and one via sampling) to assess
controller robustness in a variety of realistic scenarios provides a first step
in unifying various tools to model and assess robustness of quantum
controllers.
