  Noise and photon loss encountered on quantum channels pose a major challenge
for reliable entanglement generation in quantum networks. In near-term
networks, heralding is required to inform endpoints of successfully generated
entanglement. If after heralding, entanglement fidelity is too low,
entanglement purification can be utilized to probabilistically increase
fidelity. Traditionally, purification protocols proceed as follows: generate
heralded EPR pairs, execute a series of quantum operations on two or more pairs
between two nodes, and classically communicate results to check for success.
Purification may require several rounds while qubits are stored in memories,
vulnerable to decoherence. In this work, we explore the notion of optimistic
purification in a single link setup, wherein classical communication required
for heralding and purification is delayed, possibly to the end of the process.
Optimism reduces the overall time EPR pairs are stored in memory. While this is
beneficial for fidelity, it can result in lower rates due to the continued
execution of protocols with sparser heralding and purification outcome updates.
We apply optimism to the entanglement pumping scheme, ground- and
satellite-based EPR generation sources, and current state-of-the-art
purification circuits. We evaluate sensitivity performance to a number of
parameters including link length, EPR source rate and fidelity, and memory
coherence time. We observe that our optimistic protocols are able to increase
fidelity, while the traditional approach becomes detrimental to it for long
distances. We study the trade-off between rate and fidelity under
entanglement-based QKD, and find that optimistic schemes can yield higher rates
compared to non-optimistic counterparts, with most advantages seen in scenarios
with low initial fidelity and short coherence times.
