Heisenberg-scaling sensitivity in the estimation of two parameters in a Mach-Zehnder interferometer

Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum resources. We propose an experimentally feasible scheme to reach Heisenberg limited sensitivity in the simultaneous estimation of two unknown phase parameters in a Mach-Zehnder interferometer by using a squeezed and a coherent state of light as input and homodyne detections at the outputs.