Single-photon-added coherent state based postselected weak measurement

We investigated precision measurements in a two-level system coupled to a single-photon-added coherent state (SPACS) under postselection measurement. We analyzed strategies for improving measurement precision, including parameter estimation and the signal-to-noise ratio (SNR) in postselected weak measurements using the photon statistics of SPACS as the meter. Our results demonstrate that SPACS-based postselected weak measurements can outperform conventional measurement schemes in terms of precision. Additionally, we explicitly introduced an alternative weak measurement method commonly applied in dispersive light-atom interactions. Our work offers a new way for addressing fundamental issues in quantum precision measurement based on photon statistics, and it provides a method for extracting the phase and phase shifts of radiation fields through the weak values of system observables.