The eavesdropping scheme proposed by W\'{ o}jcik [Phys. Rev. Lett. { \bf 90},157901(2003)] on the quantum communication protocol of Bostr\"{ o}m and Felbinger [Phys. Rev. Lett. { \bf 89}, 187902(2002)] is improved by constituting a new set of attack operations. The improved scheme only induces half of the eavesdropping losses in W\'{ o}jcik's scheme, therefore, in a larger domain of the quantum channel transmission efficiency $\eta$, i.e., [0,75%], the eavesdropper Eve can attack all the transmitted bits. Comparing to W\'{ o}jcik's scheme, in the improved scheme the eavesdropping (legitimate) information gain does not vary in the $\eta$ domain of [0, 50%], while in the $\eta$ domain of (50%, 75%] the less eavesdropping losses induce more eavesdropping information gains, for Eve can attack { \it all} the transmitted bits and accordingly eavesdropping information gains do { \it not} decrease. Moreover, for the Bostr\"{ o}m-Felbinger protocol, the insecurity upper bound of $\eta$ presented by W\'{ o}jcik is pushed up in the this paper, that is, according to W\'{ o}jcik's eavesdropping scheme, the Bostr\"{ o}m-Felbinger protocol is not secure for transmission efficiencies lower than almost 60%, while according to the improved scheme, it is not secure for transmission efficiencies lower than almost 80%.
Categories: quant-ph