In Acin's paper, it is mentioned that, given Eve chooses to do a collective attack (which roughly means Eve applies the same attack to each system of Alice and Bob, and that the devices with Alice and Bob are memoryless so they behave independently and identically at each step of the protocol), an optimal collective attack corresponds to the case where the tripartite state $\vert \psi_{ABE} \rangle$ is the purification of the bipartite state $\rho_{AB}$ shared by Alice and Bob.

Why is that so? I get the point that this means including Eve's knowledge would make noisy state $\rho_{AB}$ into a noiseless state $\vert \psi_{ABE} \rangle$, but this just says that Eve has some knowledge. How does this translate to it being a requirement for a collective attack to be "optimal"?

In Acin's paper (arXiv), it is mentioned that, given Eve chooses to do a collective attack (which roughly means Eve applies the same attack to each system of Alice and Bob, and that the devices with Alice and Bob are memoryless so they behave independently and identically at each step of the protocol), an optimal collective attack corresponds to the case where the tripartite state $\vert \psi_{ABE} \rangle$ is the purification of the bipartite state $\rho_{AB}$ shared by Alice and Bob.

Why is that so? I get the point that this means including Eve's knowledge would make noisy state $\rho_{AB}$ into a noiseless state $\vert \psi_{ABE} \rangle$, but this just says that Eve has some knowledge. How does this translate to it being a requirement for a collective attack to be "optimal"?