  Distributing entangled states over potentially long distances provides a key
resource for many protocols in quantum communication and quantum cryptography.
Ideally, this should be implemented in a heralded manner. By starting with four
single-photon states, we cascade two single-photon path-entangled states, coded
in orthogonal polarizations, to distribute and herald polarization entanglement
in a single quantum repeater link architecture. By tuning the input states to
minimize (local) losses, the theoretically achievable fidelity to the target
state without postselection approaches 1, while sacrificing heralding rates. We
achieve a fidelity to the target state of over 95% after postselection,
providing a benchmark for the experimental control. We show that the fidelity
of the heralded state without postselection scales predictably and also
identify various practical challenges and error sources specific to this
architecture, and model their effects on the generated state. While our
experiment uses probabilistic photon-pair sources based on spontaneous
parametric down-conversion, many of these problems are also relevant for
variants employing deterministic photon sources.
