Robust quantum sensing via statistics*

Many quantum sensing algorithms exist for measuring a broad range of signals, for example low-frequency signals [1] or high-frequency signals [2]. However, for signals with limited coherence times, such methods are insufficient, since long measurements average the signals to zero. Here, we propose and analyze a method to robustly detect the amplitude of such signals, which protects the result from phase and frequency changes, and can account for amplitude distributions.

In our method, we measure the standard deviation of the signal instead of the amplitude. We show that this has the same sensitivity as conventional methods for a high signal-to-noise ratio (SNR), and goes towards an N^1/4 (N: number of data points) dependence for a low SNR. Moreover, the memory requirements and computational complexity of this method are low, which suits long measurements.

One important application is the search for light dark matter [3]. For the axion and dark photon candidates, the dark matter field can be measured with nitrogen-vacancy centers as an effective periodic magnetic field with a limited coherence time. Given the minuscule signals, long measurement times are required, which makes the proposed method ideal.

[1] Phys. Rev. Appl. 18, 034058 (2022).

[2] Phys. Rev. X 12, 021061 (2022).

[3] arXiv:2302.12756 (2023).