Shor-Preskill-type security proof for quantum key distribution without public announcement of bases

Abstract

We give a Shor-Preskill-type security proof to quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, which is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded.