For coherent states in a Mach-Zehnder interferometer, postselected dark-port detection yields an amplified phase shift that matches weak-value amplification in the AAV limit, but with shot-noise (1/√N) scaling rather than Heisenberg scaling.
Further, one can modulate the transmission- reflection coefficient of BS2
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Postselected amplification applied to Mach-Zehnder-interferometer for phase shift measurement of optical coherent states
For coherent states in a Mach-Zehnder interferometer, postselected dark-port detection yields an amplified phase shift that matches weak-value amplification in the AAV limit, but with shot-noise (1/√N) scaling rather than Heisenberg scaling.