Here's an interesting related aside: the likely design of a practical quantum internet would make QKD totally trivial. What a quantum internet would do is deliver kinda-noisy entangled Bell pairs to endpoints that wanted to communicate. The endpoints would then purify [1] this kinda-noisy entanglement into actually-good entanglement (e.g. from 1% error to 0.0000000000001% error). The purified Bell pairs can then be consumed in order to transmit qubits [2]. However, because of the monogamy of entanglement [3], the purification process must detect and correct eavesdropping (or else fail to produce output). So, once you have a sufficiently purified Bell pair, it can be measured to get a bit that can be used as a one time pad. (That said, this does still assume you have an authenticated channel! Purification requires communication, because without authentication you can be man-in-the-middle'd.)
[1]: https://en.wikipedia.org/wiki/Entanglement_distillation