  With the assistance of weak cross-Kerr nonlinearities, we introduce an
optical scheme to fuse two small-size polarization entangled W states into a
large-scale W state without qubit loss, i.e.,$\mathrm{W}_{n+m}$ state can be
generated from an $n$-qubit W state and a $m$-qubit W state. To complete the
fusion task, two polarization entanglement processes and one spatial
entanglement process are applied. The fulfillments of the above processes are
contributed by a cross-Kerr nonlinear interaction between the signal photons
and a coherent state via Kerr media. We analyze the resource cost and the
success probability of the scheme. There is no complete failure output in our
fusion mechanism, and all the garbage states are recyclable. In addition, there
is no need for any controlled quantum gate and any ancillary photon, so it is
simple and feasible under the current experiment technology.
