Fusion of atomic W-like states in cavity QED systems

It is well-known that maximally entangled GHZ states can achieve perfect teleportation and superdense coding, whereas maximally entangled W states cannot. However, it has been demonstrated that there exists a special class of non-maximally entangled W states, called as W-like states, which can overcome this limitation. Therefore, it is of great significance to prepare such W-like states for efficient quantum communication. Here, we propose two kinds of novel and efficient fusion schemes for atomic W-like states based on the large-detuning interactions between several atoms and a single-mode cavity field, with which large-scale atomic \(|\mathcal {W}_{N+M-1}\rangle \) $|{\mathcal{W}}_{N+M-1}⟩$ and \(|\mathcal {W}_{N+M+T-2}\rangle \) $|{\mathcal{W}}_{N+M+T-2}⟩$ states can be prepared, respectively, from two small-scale atomic \(|\mathcal {W}_{N}\rangle \) $|{\mathcal{W}}_N⟩$ and \(|\mathcal {W}_{M}\rangle \) $|{\mathcal{W}}_M⟩$ states and three small-scale atomic \(|\mathcal {W}_{N}\rangle \) $|{\mathcal{W}}_N⟩$ , \(|\mathcal {W}_{M}\rangle \) $|{\mathcal{W}}_M⟩$ and \(|\mathcal {W}_{T}\rangle \) $|{\mathcal{W}}_T⟩$ states, by detecting the states of one or two of the fused atoms. Particularly, although the fusion process of our scheme involves particle loss, the corresponding success probability is high and fixed, which may induce high fusion efficiency. Furthermore, through the investigation of the resource cost and feasibility analysis, our protocol is simple and feasible under the current experimental conditions. All these suggest that it provides an alternative strategy for preparing large-scale atomic W-like states for perfect teleportation and superdense coding.