  We report the fusion of photons from two independent photonic crystal fiber
sources into polarization entangled states using a fiber-based polarizing beam
splitter. We achieve fidelities of up to F = 0.74 $\pm$ 0.01 with respect to
the maximally entangled Bell state \phi+ using a low pump power of 5.3mW with a
success rate of 3.2 four-fold detections per second. By increasing the pump
power we find that success rates of up to 111.6 four-folds per second can be
achieved, with entanglement still present in the fused state. We characterize
the fusion operation by providing a full quantum process reconstruction. Here a
model is developed to describe the generation of entanglement, including the
main causes of imperfection, and we show that this model fits well with the
experimental results. Our work shows how non-ideal settings limit the success
of the fusion, providing useful information about the practical requirements
for an operation that may be used to build large entangled states in bulk and
on-chip quantum photonic waveguides.
