Reply to Comment on 'Semiquantum-key distribution using less than four quantum states'

In the preceding Comment [Phys. Rev. A 83, 046301 (2011)], Boyer and Mor pointed out that the first conclusion of Lemma 1 in our paper [X. Zou, D. Qiu, L. Li, L. Wu, and L. Li, Phys. Rev. A 79, 052312 (2009)] is not correct, and therefore, the proof of Theorem 5 based on Lemma 1 is wrong. Furthermore, they gave a direct proof for Theorem 5 and affirmed the conclusions in our original paper. In this Reply, we admit the first conclusion of Lemma 1 is not correct, but we need to point out that the second conclusion of Lemma 1 is correct. Accordingly, all the proofs for Lemma 2, Lemma 3, and Theorems 3-6 are based only on the second conclusion of Lemma 1 and therefore are correct.