Having a quantum internet with quantum repeaters and end nodes, even if it works at its best conditions, is, sadly, far from ideal. In this video, entanglement distillation and how we can refine our shared entanglement states before proceeding to any protocol are explained. Secondly, there's an example with very well known quantum states.
What if the state Alice and Bob wanted to share is different? What changes in the protocol?
Do you think that increasing the number of rounds, keeping the source pair the same, will get you to higher and higher fidelity states?