Constraints on recovering quantum information after erasure

Suppose that we encode quantum information into $ n $ physical carriers.

With what probabilities can we perfectly recover the quantum information after sets of carriers have been erased?

This question arises in the study of quantum erasure channels, for which M.B.

Hastings conjectured that if each carrier is independently erased with probability $ t \geq 1/2 $, then it is impossible to recover the quantum information with asymptotically vanishing error and probability $ > 1-t $.

We prove this conjecture by establishing new no-cloning constraints on realizable recovery probabilities.