“…If all the other states φ i are not very "different" from the target state |Ψ , i.e., Ψ|φ i ∼ 1, then the reduction in fidelity from measuring the mixed state ρ, as opposed to the heralded ensemble of target states, will not be severe. However, in many situations, there will be some states φ i that are nearly orthogonal to |Ψ , and have high probabilities r i of being generated, and this will dramatically decrease the measured fidelity 29. To illustrate our point, we assume here a simple entanglement-swapping-based approach to distributing entanglement, in which the adjacent nodes each attempt to become entangled with their immediate neighbours (stopping once they have succeeded), and where the protocol is reset once every pair of adjacent nodes shares an entangled qubit pair.…”