Mitigating unbalanced loss in entanglement assisted absorptive measurements with a phase-sensitive amplifier

Correlated interferometry offers various advantages in precision measurements, such as sub-shot noise sensitivity, high resolution, and prevention of detector saturation benefiting from dark output. In certain practical scenarios, e.g. absorptive measurement, there is usually unbalanced loss between the probe and reference beams, which destroys the correlation and remains a significant obstacle in the efficient application of entanglements. Here, we study the performance of a nonlinear interferometer whose arms experience unbalanced loss and demonstrate the use of a phase-sensitive amplifier in the sensing or reference arms to amplify or squeeze the light field, which can both reduce the degradation of quantum enhancement from unbalanced absorption in a lossy environment. We find that the loss after amplification, i.e. from imperfect interferometry and detection, can be mitigated when the phase-sensitive amplifier is placed at the sensing arm and functions as a noiseless amplifier. Our approach may be helpful to the practical application of quantum-enhanced absorptive measurement.