Finite key size analysis of two-way quantum cryptography

Quantum cryptographic protocols solve the longstanding problem of distributing a shared secret string to two distant users by typically making use of one-way quantum channel. However, alternative protocols exploiting two-way quantum channel have been proposed for the same goal and with potential advantages. Here we overview a security proof for two-way quantum key distribution protocols, against the most general eavesdropping attack, that utilize an entropic uncertainty relation. Then, by resorting to the `smooth' version of involved entropies, we extend such a proof to the case of finite key size. The results will be compared to those available for one-way protocols showing some advantages.