Noiseless attack on certain quantum key distribution protocols

The information-disturbance tradeoff lies at the heart of quantum key distribution (QKD), allowing a sender and a receiver to monitor eavesdropping in the communication channel by checking for errors in the transmission. Even so, here we show that for a class of QKD protocols based on the principle of interaction-free measurement, an eavesdropper Eve can obtain partial information noiselessly, i.e., in such a way that the disturbance produced does not show up during the error checking. The proposed attack is shown to be the optimal individual noiseless attack. An implication of the noiselessness is that even though error correction is not required, privacy amplification (PA) is necessary. For example, in the case of the protocol of [T.-G. Noh, PRL 103, 230501 (2009)], the compression factor of PA is 0.68 in the case of an individual, noiseless attack. For the noisy generalization of the above attack, where Eve introduces noise into the communication channel without adding noise to the eavesdropping channel, the security requirement entails a lower bound on the noise threshold of about 11%, assuming that the transmitted particles are single photons.