Quantum multiparameter metrology with generalized entangled coherent state

We propose a generalized form of entangled coherent states (ECS) and apply them in a multi-arm optical interferometer to estimate multiple phase shifts. We obtain the quantum Cramer-Rao bounds for both the linear and nonlinear parameterization protocols. Through the analysis, we find that, utilizing the simultaneous estimation, this generalized form of ECS gives a better precision than the generalized NOON states Phys. Rev. Lett. 111, 070403 (2013). Moreover, comparing with the independent estimation, both the linear and nonlinear protocols have the same advantage in the relation to the number of the parameters.