Saturating the quantum Cramér-Rao bound using LOCC*

The quantum Cramér-Rao bound (QCRB) provides an ultimate precision limit allowed by quantum mechanics in parameter estimation. Given any quantum state dependent on a single parameter, there is always a positive-operator valued measurement (POVM) saturating the QCRB. However, the QCRB-saturating POVM cannot always be implemented efficiently, especially in multipartite systems. In this talk, we show that the POVM based on local operations and classical communication (LOCC) is QCRB-saturating for arbitrary pure states or rank-two mixed states with varying probability distributions over fixed eigenbasis. We also analyze the robustness of our LOCC protocol against noise and show how it can be made noise-resilient. Finally, a four-qubit system is studied as an example of a non-trivial LOCC protocol saturating the QCRB. For details, see ArXiv: 1809.06017.