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

Upper Bound of Collective Attacks on Quantum Key Distribution