A measurement scheme consisting of a displacement operation and photon counting, which is often referred to as
displaced-photon counting, provides near-optimal performance for coherent states discrimination problem.
Due to an improvement of the photon counters, displaced-photon counting technique can be implemented with
high efficiency in recent years.
It is interesting to extend displaced-photon counting scheme to other optical strategies such as
phase sensing.
In our study, we apply displaced-photon counting to phase estimation of coherent state.
We numerically show that our detection scheme can reduce an estimation error less than that of dyne measurements
and experimentally demonstrate the scheme by using superconductor single photon detector.