We study Greenberger-Horne-Zeilinger--type (GHZ-type) and
W-type three-mode entangled coherent states. Both types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for
W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate
W-type entangled coherent states in free-traveling optical fields. The required resources for the generation are a single-photon source, a coherent state source, beam splitters, phase shifters, photodetectors, and Kerr nonlinearities. Our scheme does not necessarily require strong Kerr nonlinear interactions; i.e., weak nonlinearities can be used for the generation of the
W-type entangled coherent states. Furthermore, it is also robust against inefficiencies of the single-photon source and the photon detectors.
We establish a new model for realization of three qubit C-NOT gate operations between two Rydberg atoms and coherent Cavity field. To exploit this C-NOT realization, we enhance m any schemes for generation of GHZ-type and W-type entangled coherent state (ECS), to prepare n-cavities GHZ- type (ECS) and n-cavities W- type (ECS). Furthermore, we find the possibility of p reparing cluster entangled coherent states using the realized three qubit C-NOT gate. Our model compared with the references schemes generation is more efficient because of simplicity of detect ing coherent fields. Also, the rigidity of the model comes fro m the smaller interaction time needed to realize the three quantum entangled systems due to the proposed interaction.