Second-order coding rates for key distillation in quantum key distribution

Understand

The security of quantum key distribution has traditionally been analyzed in either the asymptotic or non-asymptotic regimes.

• In this paper, we provide a bridge between these two regimes, by determining second-order coding rates for key distillation in quantum key distribution under collective attacks.
• Our main result is a formula that characterizes the backoff from the known asymptotic formula for key distillation -- our formula incorporates the reliability and security of the protocol, as well as the mutual information variances to the legitimate receiver and the eavesdropper.
• In order to determine secure key rates against collective attacks, one should perform a joint optimization of the Holevo information and the Holevo information variance to the eavesdropper.