We analyze simultaneous quantum estimations of multiple parameters with postselection measurements in terms of a trade-off relation. The system, or a sensor, is characterized by a set of parameters, interacts with a measurement apparatus (MA), and then is postselected onto a set of orthonormal final states. Measurements of the MA yield an estimation of the parameters. We first derive classical and quantum Cramér–Rao lower bounds and then discuss their archivable condition and the trade-offs in the postselection measurements, in general, including the case when a sensor is in a mixed state. Its whole information can, in principle, be obtained via the MA, which is not possible without postselection. We then apply the framework to simultaneous measurements of phase and its fluctuation as an example.

中文翻译：

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具有后选测量的多参数量子计量

我们根据权衡关系分析了多个参数与同时选择后测量的同时量子估计。该系统或传感器的特征在于一组参数，它与测量设备（MA）交互，然后被后选到一组正交的最终状态。MA的测量产生参数的估计。我们首先得出经典和量子Cramér-Rao的下界，然后讨论它们的可归档条件和后期选择测量中的权衡，通常包括传感器处于混合状态的情况。原则上，它的全部信息可以通过MA获得，没有后选择是不可能的。然后，我们将该框架应用于同时测量相位及其波动的示例。