Security of Quantum Key Distribution Against All Collective Attacks

Security of quantum key distribution against sophisticated attacks is among the most important issues in quantum information theory. In this work we prove security against a very important class of attacks called collective attacks (under a compatible noise model) which use quantum memories and gates, and which are directed against the final key. Although attacks stronger than the collective attacks can exist in principle, no explicit example was found and it is conjectured that security against collective attacks implies also security against any attack.