  Quantum hypothesis testing plays a pivotal role in quantum technologies,
making decisions or drawing conclusions about quantum systems based on observed
data. Recently, quantum control techniques have been successfully applied to
quantum hypothesis testing, enabling the reduction of error probabilities in
the task of distinguishing magnetic fields in presence of environmental noise.
In real-world physical systems, such control is prone to various channels of
inaccuracies. Therefore improving the robustness of quantum control in the
context of quantum hypothesis testing is crucial. In this work, we utilize
optimal control methods to compare scenarios with and without accounting for
the effects of signal frequency inaccuracies. For parallel dephasing and
spontaneous emission, the optimal control inherently demonstrates a certain
level of robustness, while in the case of transverse dephasing with an
imperfect signal, it may result in a higher error probability compared to the
uncontrolled scheme. To overcome these limitations, we introduce a robust
control approach optimized for a range of signal noise, demonstrating superior
robustness beyond the predefined tolerance window. On average, both the optimal
control and robust control show improvements over the uncontrolled schemes for
various dephasing or decay rates, with the robust control yielding the lowest
error probability.
