Recently, a DC magnetometry protocol utilizing N-spin-ensemble superradiance was proposed. This method physically amplifies the acquired signal, suppressing estimation errors from measurement noise and achieving O(1/N) precision scaling when measurement noise dominates quantum fluctuations. However, quantum metrology is generally vulnerable to independent Markovian pure dephasing. For instance, the scaling of Greenberger-Horne-Zeilinger (GHZ) state-based magnetometry deteriorates from O(1/N) to O(1/N). Although pure dephasing likely degrades superradiant sensing, its quantitative impact remains unclear. Here, we investigate the effect of independent Markovian pure dephasing on this protocol using numerical simulations and mean-field analysis. We demonstrate that, in the large-N limit, the estimation error increase is limited to a constant factor. This sharply contrasts with GHZ-state-based sensing, where the error increases by a factor of N. Our analytical solutions elucidate the physical origin of this robustness qualitatively. These findings establish the high robustness of superradiance-based DC magnetometry against independent Markovian pure dephasing.
We analyze the multitime statistics associated with pure dephasing systems repeatedly probed with sharp measurements, and search for measurement protocols whose statistics satisfy the Kolmogorov consistency conditions possibly up to a finite order. We find a rich phenomenology of quantum dephasing processes which can be interpreted in classical terms. In particular, if the underlying dephasing process is Markovian, we find sufficient conditions under which classicality at every order can be found: this can be reached by choosing the dephasing and measurement basis to be fully compatible or fully incompatible, that is, mutually unbiased bases (MUBs). For non-Markovian processes, classicality can only be proven in the fully compatible case, thus revealing a key difference between Markovian and non-Markovian pure dephasing processes.