W states fusion via polarization-dependent beam splitter

Based on the polarization-dependent beam splitter (PDBS), we propose an optical scheme to fuse small-size polarization entangled W states into a large-scale W states. With the present scheme, two \(W_{m+n+t-2}\) states can be created from an n-qubit W state, an m-qubit W state and a t-qubit W state, and two \(W_{m+n+t+q-3}\) states can be generated from \(W_m\), \(W_n\), \(W_t\) and \(W_q\) states. In the previous fusion schemes, only one particle from each initial W state is allowed to enter the fusion mechanism, but with the progress of experimental technology, two particles can be extracted. In this case, the W states fusion of our scheme will be realized without any ancillary particles and controlled quantum gate. In addition, compared with the one target W state obtained in previous preparation schemes, our scheme can generate two large-scale W states, which effectively improve the success rate of generating target W state. The ability to generate two target W states makes our scheme have a distinct advantage in preparing W states with larger particle numbers. This preparation mechanism also can be generalized to the case of fusing more different or same particles W states.