Postselected amplification applied to Mach-Zehnder-interferometer for phase shift measurement of optical coherent states

We propose a postselected amplification scheme for phase shift measurement of optical coherent states when passing through the Mach-Zehnder-interferometer (MZI). Different from the usual weak-value-amplification(WVA) formulation, the which-path states of the MZI cannot be described as sub-system states entangled withtwo optical coherent states. However, we obtain the same phase amplification result of the usual WVA in theAharonov-Albert-Vaidman (AAV) limit, but beyond this limit, the result is essentially different. We explicitlycarry out the amplified phase shift, which can be extracted out from the field-quadrature measurement in the darkport of the MZI. We also evaluate the performance quality of the proposed scheme, and analyze the technicaladvantages by considering possible errors in the quadrature measurement.