The security of the decoherence-free version of the Bennett-Brassard 1984 (BB84) protocol [A. Cabello, Phys. Rev. A 75, 020301 (2007)] is analyzed and shown to be vulnerable under the intercept-resend attack. We propose two improved versions of this protocol. Both improvements remain the performance of robustness against collective noise and refuse the security flaw. Especially, the second improvement, which is called four-qubit decoherence-free (DF) BB84 protocol, not only remains all characteristics of the original protocol but also has a higher efficiency. We also give a detailed security proof of four-qubit DF BB84 protocol.

• Received 23 May 2009

DOI:https://doi.org/10.1103/PhysRevA.80.032321