The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that it is secure against general attacks: even if an adversary performs a complicated attack involving all of the rounds of the protocol, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave the same in each round. Using a recently developed information-theoretic tool called generalised entropy accumulation, we show that for a very broad class of QKD protocols, security against collective attacks implies security against general attacks. Compared to existing techniques such as the quantum de Finetti theorem or a previous version of entropy accumulation, our result can be applied much more broadly and easily: it does not require special assumptions on the protocol such as symmetry or a Markov property between rounds, its bounds are independent of the dimension of the underlying Hilbert space, and it can be applied to prepare-and-measure protocols directly without switching to an entanglement-based version.
