Preparation of entangled W states based on the cavity QED system

We present a qubit-loss-free (QLF) fusion scheme for generating large-scale atom W states in cavity quantum electrodynamics (QED) system. Compared to the most current fusion schemes which are conditioned on the case where one particle can be extracted from each initial W state to the fusion process, our scheme will access one or two particles from each W state. Based on the atom–cavity-field detuned interaction, three |W〉_n+m+t states can be generated from the |W〉_n, |W〉_m, and |W〉_t states with the help of two auxiliary atoms, and three |W〉_n+m+t+q states can be generated from |W〉_n, |W〉_m, |W〉_t, and a |W〉_q state with the help of three auxiliary atoms. Comparing the numerical simulations of the resource cost of fusing three small-size W states based on the previous schemes, our fusion scheme seems to be more efficient. This QLF fusion scheme can be generalized to the case of fusing k different or identical particle W states. Furthermore, with no qubit loss, it greatly reduces the number of fusion steps and prepares W states with larger particle numbers.