I was skimming the paper and came to this: > This transformation is like an AND gate - it ignores the index qubit and places the flag qubit in the state |1> if and only if either of the original components had the state |1> for the flag qubit.
Shouldn't that be an OR gate? Not only does the description above say "if and only if either of the original components had the state |1>", which is an OR, but the truth table listed above shows the same thing for the flag qubit.
Of course, one could say it's an AND on the |0> states, which is just De Morgan's law, but that's pretty awkward phrasing.
Demorgan's theorem says AND and OR are equivalent, and only depend upon the polarity of the bits. So if "state |1>" is a binary zero, AND is the proper logical operator.
Are you sure you're looking at the right paper? I don't find the sentence you mention in the paper.