We discuss the problem of estimating a frequency via [Formula: see text]-qubit probes undergoing independent dephasing channels that can be continuously monitored via homodyne or photo-detection. We derive the corresponding analytical solutions for the conditional states, for generic initial states and for arbitrary efficiency of the continuous monitoring. For the detection strategies considered, we show that: (i) in the case of perfect continuous detection, the quantum Fisher information (QFI) of the conditional states is equal to the one obtained in the noiseless dynamics; (ii) for smaller detection efficiencies, the QFI of the conditional state is equal to the QFI of a state undergoing the (unconditional) dephasing dynamics, but with an effectively reduced noise parameter.

中文翻译：

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具有连续监测的独立相移通道条件状态的量子频率估计

我们讨论了通过[公式：见文本]-qubit 探针估计频率的问题，这些探针经历独立的相移通道，可以通过零差或光电检测连续监测。我们为条件状态、通用初始状态和连续监测的任意效率推导出相应的解析解。对于所考虑的检测策略，我们表明：（i）在完美连续检测的情况下，条件状态的量子Fisher信息（QFI）等于在无噪声动力学中获得的信息；(ii) 对于较小的检测效率，条件状态的 QFI 等于经历（无条件）移相动态的状态的 QFI，但噪声参数有效降低。