Postselected amplification applied to the 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 subsystem states entangled with two optical coherent states. However, we obtain the same phase amplification result of the usual WVA in the Aharonov-Albert-Vaidman limit but, beyond this limit, the result is essentially different. We explicitly carry out the amplified phase shift, which can be extracted out from the field-quadrature measurement in the dark port of the MZI. We also evaluate the performance quality of the proposed scheme and analyze the technical advantages by considering possible errors in the quadrature measurement.