Quantum metrology calculates the ultimate precision of all estimation strategies, measuring what is their root-mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover; namely, we derive an information-theoretic quantum metrology. In this setting, we redefine “Heisenberg bound” and “standard quantum limit” (the usual benchmarks in the quantum estimation theory) and show that the former can be attained only by sequential strategies or parallel strategies that employ entanglement among probes, whereas parallel-separable strategies are limited by the latter. We highlight the differences between this setting and the RMSE-based one.

中文翻译：

---

数字量子估计

量子计量计算所有估计策略的最终精度，并测量其均方根误差（RMSE）和其Fisher信息。相反，在这里，我们询问可以恢复多少位参数；即，我们得出了一个信息理论的量子计量学。在这种情况下，我们重新定义了“海森堡界”和“标准量子极限”（量子估计理论中通常的基准），并表明前者只能通过采用探针间纠缠的顺序策略或并行策略来实现，而并行-可分离的策略受到后者的限制。我们着重说明此设置与基于RMSE的设置之间的区别。