Robust Quantum Control for Quantum Hypothesis Testing*

Quantum hypothesis testing is a crucial component of quantum technologies, involving the assessment of quantum systems based on observed data. Recent advancements have seen the successful application of quantum control techniques in this context, allowing for the reduction of error rates when distinguishing magnetic fields in the presence of environmental noise. Nevertheless, real-world physical systems introduce various sources of inaccuracies in quantum control, emphasizing the need to enhance its robustness in quantum hypothesis testing. In this study, we employ optimal control methods to compare scenarios with and without accounting for signal frequency inaccuracies. The optimal control exhibits inherent robustness for parallel dephasing and spontaneous emission, but when dealing with transverse dephasing and an imperfect signal, it may lead to a higher error probability compared to uncontrolled schemes. To address these limitations, we introduce a robust control approach optimized for a range of signal noise, demonstrating superior resilience beyond predefined tolerance limits. On average, both the optimal and robust control strategies show enhancements over uncontrolled schemes for various dephasing or decay rates, with the robust control achieving the lowest error probability.