Enhancing signal and signal-to-noise ratio with post-selection and nonclassical states

We propose a weak measurement scheme with post-selection based on the cross-Kerr interaction between two optical fields. We demonstrate that our scheme can measure smaller physical effects and obtain a larger signal-to-noise ratio compared to the weak measurement scheme without post-selection. We also show that the initial pointer states with nonclassical properties can increase the successful post-selection probability, offer a bigger signal-to-noise ratio compared to the coherent states. •A new post-selected weak measurement scheme with based on the cross-Kerr interaction is proposed.•The initial pointer states with nonclassical properties can increase the successful post-selection probability.•The initial pointer states with nonclassical properties can offer a bigger SNR ratio compared to the coherent states.