Tetrationally Compact Entanglement Purification

This paper shows that entanglement can be purified using very little storage, assuming the only source of noise is in the quantum channel being used to share the entanglement. Entangled pairs with a target infidelity of $\epsilon$ can be created in $\tilde{O}(\log \frac{1}{\epsilon})$ time using $O(\log^{\ast} \frac{1}{\epsilon})$ storage space, where $\log^{\ast}$ is the iterated logarithm. This is achieved by using multiple stages of error detection, with boosting within each stage. For example, the paper shows that 11 qubits of noiseless storage is enough to turn entanglement with an infidelity of $1/3$ into entanglement with an infidelity of $10^{-1000000000000000000000000000}$.