Simultaneous estimation of three parameters with Heisenberg scaling sensitivity in a two-channel optical network

This work presents a quantum sensing interferometric scheme for the simultaneous estimation of multiple parameters at the ultimate quantum scaling precision in a two-mode optical network. This scheme is experimentally feasible because it employs input Gaussian states such as squeezed and coherent states and a relatively low number of experimental runs. We focus on the precise and simultaneous measurement of two unknown phase shifts and an unknown beam splitter reflectivity, achieving Heisenberg scaling sensitivity in all three parameters without any constraints on the parameter values.