Optimistic Entanglement Purification With Few Quantum Memories

Entanglement generation over large distances is a challenging task due to photon loss, which grows exponentially with link length (e.g., optical fiber). Moreover, EPR pair generation over noisy channels results in imperfect states. Thus, a link is associated with a success probability and an initial fidelity for successfully-generated entanglement. Over time, fidelity de-creases due to environmental noise. Entanglement purification is a way of probabilistically increasing state fidelity. Traditionally, purification protocols perform the following steps: generate two or more EPR pairs between two nodes, execute a series of quantum gates on both sides, and exchange results via classical messages. In this work, we propose a twist on the original entanglement pumping scheme, wherein a fixed number of purification steps are performed successively, before the classical information exchange. This modification introduces optimism to the overall procedure, such that classical communication is performed only at the end, to check the measurement results. The protocol is also optimistic about entanglement generation and does not wait for heralding signals before attempting purification. We study the effect of being optimistic on fidelity and the waiting time to generate an entangled pair as a function of the distance between network nodes. We observe an improvement in both fidelity and expected waiting time. We also study the effect of the number of purification steps on fidelity and latency and observe that typically no more than two or three purification steps are needed when limited by only two memories.