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Entangled states can potentially be used to outperform the standard quantumlimit which every classical sensor is bounded by. However, entangled states arevery susceptible to decoherence, and so it is not clear whether one can reallycreate a superior sensor to classical technology via a quantum strategy whichis subject to the effect of realistic noise. This paper presents aninvestigation of how a quantum sensor composed of many spins is affected byindependent dephasing. We adopt general noise models including non-Markovianeffects, and in these noise models the performance of the sensor dependscrucially on the exposure time of the sensor to the field. We have found that,by choosing an appropriate exposure time within non-Markovian time region, anentangled sensor does actually beat the standard quantum limit. Sinceindependent dephasing is one of the most typical sources of noise in manysystems, our results suggest a practical and scalable approach to beating thestandard quantum limit.

Magnet field sensing beyond the standard quantum limit under the effect of decoherence