Reconstructing the Profile of Time-Varying Magnetic Fields With Quantum Sensors

TL;DR

This paper provides a detailed theoretical analysis of reconstructing time-varying magnetic fields using quantum sensors and Walsh functions, emphasizing sensitivity, data compression, and noise robustness.

Contribution

It introduces a novel Walsh-based reconstruction method with sensitivity analysis, error characterization, and data compression techniques for quantum magnetic field sensing.

Findings

Walsh basis properties enhance reconstruction accuracy

Sensitivity analysis informs error bounds

Data compression improves resource efficiency

Abstract

Quantum systems have shown great promise for precision metrology thanks to advances in their control. This has allowed not only the sensitive estimation of external parameters but also the reconstruction of their temporal profile. In particular, quantum control techniques and orthogonal function theory have been applied to the reconstruction of the complete profiles of time-varying magnetic fields. Here, we provide a detailed theoretical analysis of the reconstruction method based on the Walsh functions, highlighting the relationship between the orthonormal Walsh basis, sensitivity of field reconstructions, data compression techniques, and dynamical decoupling theory. Specifically, we show how properties of the Walsh basis and a detailed sensitivity analysis of the reconstruction protocol provide a method to characterize the error between the reconstructed and true fields. In addition, we prove various results about the negligibility function on binary sequences which lead to data compression techniques in the Walsh basis and a more resource-efficient reconstruction protocol. The negligibility proves a fruitful concept to unify the information content of Walsh functions and their dynamical decoupling power, which makes the reconstruction method robust against noise.