  Evaluating the theoretical limit of the amount of information Eve can steal
from a quantum key distribution protocol under given conditions is one of the
most important things that need to be done in security proof. In addition to
source loopholes and detection loopholes, channel attacks are considered to be
the main ways of information leakage, while collective attacks are considered
to be the most powerful active channel attacks. Here we deduce in detail the
capability limit of Eve's collective attack in non-entangled quantum key
distribution, like BB84 and measurement-device-independent protocols, and
entangled quantum key distribution, like device-independent protocol, in which
collective attack is composed of quantum weak measurement and quantum
unambiguous state discrimination detection. The theoretical results show that
collective attacks are equivalent in entangled and non-entangled quantum key
distribution protocols. We also find that compared with the security proof
based on entanglement purification, the security proof based on collective
attack not only improves the system's tolerable bit error rate, but also
improves the key rate.
