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When estimating the phase of a single mode, the quantum Fisher informationfor a pure probe state is proportional to the photon number variance of theprobe state. In this work, we point out particular states that offer photonnumber distributions exhibiting a large variance, which would help to improvethe local estimation precision. These theoretical examples are expected tostimulate the community to put more attention to those states that we found,and to work towards their experimental realization and usage in quantummetrology.

Using states with a large photon number variance to increase quantum Fisher information in single-mode phase estimation