On page 7 of this paper by Sebens and Carroll they discuss the diagonal terms of the reduced density matrix during decoherence. I am very confused. I thought the diagonal terms are the only ones that remain after decoherence occurs, but they say "The diagonal terms have dropped out" after the measurement and before the measurement they say "the diagonal terms of the reduced density matrix are non-zero". Do I have this all backwards or am I misunderstanding the argument?
I looked at the paper and I believe it is a typo both times -- should say off diagonal. The reason I think so is because if you look at the equations it is actually the diagonal terms that are left and the off ones drop out. Also, note what they says in the parenthesis: "the diagonal terms of the reduced density matrix (the middle two terms of the sum in the second line of (5))" and when you look at the equation these are actually the off diagonal ones.