Efficient quantum secure communication with a publicly known key

This paper presents a simple way for an eavesdropper to eavesdrop freely the secret message in the experimental realization of quantum communication protocol proposed by Beige {\em et al} (2002 \emph{Acta Phys. Pol.} A \textbf{101} 357). Moreover, it introduces an efficient quantum secure communication protocol based on a publicly known key with decoy photons and two biased bases by modifying the original protocol. The total efficiency of this new protocol is double that of the original one. With a low noise quantum channel, this protocol can be used for transmitting a secret message. At present, this protocol is good for generating a private key efficiently.