Optical generation of a hybrid entangled state via an entangling single-photon-added coherent state

We propose a feasible scheme based on the nonlinear Mach-Zehnder interferometer to realize the optical entanglement of a single-photon-added coherent state and show that, besides the Sanders entangled coherent state, the entangled single-photon-added coherent state also leads to new forms of hybrid entanglement of the quantum Fock state and the classical coherent state. We probe the essential difference between two types of hybrid entangled states. This hybrid entangled state provides a novel link between the discrete-variable and the continuous-variable entanglement in a natural way. Finally, we give a qualitative analysis of the losses in our scheme.