Preparing large-scale maximally entangled W states in optical system

We propose an optical scheme to prepare large-scale maximally entangled W states by fusing arbitrary-size polarization entangled W states via polarization-dependent beam splitter. Because most of the currently existing fusion schemes are suffering from the qubit loss problem, that is the number of the output entangled qubits is smaller than the sum of numbers of the input entangled qubits, which will inevitably decrease the fusion efficiency and increase the number of fusion steps as well as the requirement of quantum memories, in our scheme, we design a effect fusion mechanism to generate W_{m + n} state from a n-qubit W state and a m-qubit W state without any qubit loss. As the nature of this fusion mechanism clearly increases the final size of the obtained W state, it is more efficient and feasible. In addition, our scheme can also generate W_{m + n + t - 1} state by fusing a W_m, a W_n and a W_t states. This is a great progress compared with the current scheme which has to lose at least two particles in the fusion of three W states. Moreover, it also can be generalized to the case of fusing k different W states, and all the fusion schemes proposed here can start from Bell state as well.