# Information Security and Cryptography Research Group

## Lower and Upper Bounds on the Secret Key Rate for QKD Protocols Using One-Way Classical Communication

### Barbara Kraus, Nicolas Gisin, and Renato Renner

Physical Review Letters, American Physical Society, vol. 95, no. 080501, Aug 2005, eprint archive: http://arxiv.org/abs/quant-ph/0410215.

We investigate a general class of quantum key distribution (QKD) protocols using one-way classical communication. We show that full security can be proven by considering only collective attacks. We derive computable lower and upper bounds on the secret key rate of those QKD protocol involving only entropies of two–qubit density operators. As an illustration of our results, we determine new bounds for the BB84, the six-state, and the B92 protocol. We show that in all these cases the first classical processing that the legitimate partners should apply consists in adding noise. This is precisely why any entanglement based proof would generally fail here.

## BibTeX Citation

@article{KrGiRe04,
author       = {Barbara Kraus and Nicolas Gisin and Renato Renner},
title        = {Lower and Upper Bounds on the Secret Key Rate for {QKD} Protocols Using One-Way Classical Communication},
journal      = {Physical Review Letters},
number       = 080501,
volume       = 95,
year         = 2005,
month        = 8,
note         = {eprint archive: http://arxiv.org/abs/quant-ph/0410215},
publisher    = {American Physical Society},
}