How does BB84 fare against an attacker who can entangle qubits?
After some consideration of Lukas' comment, it seems I haven't thought this through.
In fact, Eve will only entangle Bob's qubit with hers if Alice chooses the diagonal basis.
However when Bob also measures the diagonal basis, a quick calculation shows he randomly measures 0 or one, with probability 1/2 each.
So even though Eve learns which bits Bob measured, she will also introduce a 25% error chance as if she had measured them, and she will be detected.