Quantum metrology in coarsened measurement reference

We investigate the role of coarsened measurement reference in quantum metrology. Coarsened measurement reference comes from the coarsened reference time and basis. When the measurement based on one common reference basis, the disadvantage can be removed by symmetry. Due to the coarsened reference basis, entangled states can not perform better than product states for large number of probe particles. Given a finite uncertainty of the coarsened reference basis, the optimal number of probe particle is obtained in estimating phase. Finally, we prove that the maximally entangled state always achieves better precision under the case of non-Markovian dephasing than that under the case of Markovian dephasing. The product state is more resistant to interference of the coarsened reference time than the entangled state.