How hard do you expect it would be to improve the heralded infidelity from 45% to 10%?

In figure 3 of the paper [1] the heralded infidelity of entanglement is reported to be around 45%. That's not good enough for computation, but it's less than 50% which means it makes purification to arbitrarily low infidelity possible. However, the conversion rates would be pretty brutal for such a high infidelity start (e.g. millions of physical pairs consumed per logical pair good enough for use in a fault tolerant computation e.g. a target logical infidelity of 1e-6 or 1e-9).

1: https://arxiv.org/pdf/2404.03723#page=4