Choice of measurement as the secret

Recently, Kalev et al. [A. Kalev, A. Mann, and M. Revzen, Phys. Rev. Lett. 110, 260502 (2013).] proposed a quantum (public) communication protocol with an interesting encoding style, where the signal is encoded in the choice of the measurement basis of one of the communicating parties (Bob) and Bob's measurement results are irrelevant for the communication. As we know, one of the main advantages of quantum technique in communication over the classical one is the higher security. Therefore, as Kalev et al. have mentioned in their paper, an interesting open question is whether one could and how to utilize this new encoding style to design a secure communication protocol, i.e., translate the choice of measurement into the secret. Here we propose a quantum key distribution protocol, which is a secure communication protocol, with this encoding style, where Bob's measurement results are still irrelevant. Furthermore, the security of the proposed protocol in the zero-error case has been proved.