We study the estimation of a single parameter characterizing families of unitary transformations acting on two systems. We consider the situation with the presence of bottleneck, i.e., only one of the systems can be measured to gather information. The estimation capabilities are related to unitaries’ generators. In particular, we establish continuity of quantum Fisher information with respect to generators. Furthermore, we find conditions on the generators to achieve the same maximum quantum Fisher information we would have in the absence of bottleneck. We also discuss the usefulness of initial entanglement across the two systems as well as across multiple estimation instances.

我们研究了表征两个系统上的unit变换族的单个参数的估计。我们考虑存在瓶颈的情况，即只能测量其中一个系统来收集信息。估计能力与unit的生成器有关。特别是，我们建立了关于生成器的量子Fisher信息的连续性。此外，我们找到了生成器上的条件，以实现与没有瓶颈时相同的最大量子Fisher信息。我们还将讨论两个系统之间以及多个估计实例之间初始纠缠的有用性。