Detection of weak magnetic fields using nitrogen-vacancy centers with maximum confidence

The problem of detection of magnetic fields using NV centers, that is, to check whether a weak magnetic field is present or not, can be tackled using quantum state discrimination theory. In this regard, we find the POVMs that maximize the confidence of any given measurement, taking the interaction time as well as decoherence into account. We apply our formalism over a wide range of scenarios encompassing constant and oscillating magnetic fields, while also using techniques such as dynamical decoupling to improve the confidence and extending our treatment to ensembles of NV centers.