Quantum hypothesis testing via robust quantum control

TL;DR

This paper develops robust quantum control strategies to improve the reliability of quantum hypothesis testing under signal inaccuracies and environmental noise, enhancing decision accuracy in quantum systems.

Contribution

It introduces a robust control method optimized for signal noise ranges, outperforming traditional optimal control and uncontrolled schemes in quantum hypothesis testing.

Findings

Robust control reduces error probabilities across various noise conditions.

Optimal control shows inherent robustness in some scenarios but not all.

Robust control outperforms other schemes in average error reduction.

Abstract

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.