Quantum fisher information of entangled coherent states in a lossy Mach - Zehnder interferometer

We give an analytical result for the quantum Fisher information of entangled coherent states in a lossy Mach-Zehnder interferometer recently proposed by Joo et al., [Phys. Rev. Lett. 107 (2011) 083601]. For small loss of photons, we find that the entangled coherent state can surpass the Heisenberg limit. Furthermore, the formalism developed here is applicable to the study of phase sensitivity of multipartite entangled coherent states.