Less eavesdropping losses induce more eavesdropping information gain

Abstract

The eavesdropping scheme proposed by Wójcik [Phys. Rev. Lett. {\bf 90},157901(2003)] on the quantum communication protocol of Boström 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 Wójcik's scheme, therefore, in a larger domain of the quantum channel transmission efficiency $η$, i.e., [0,75%], the eavesdropper Eve can attack all the transmitted bits. Comparing to Wójcik's scheme, in the improved scheme the eavesdropping (legitimate) information gain does not vary in the $η$ domain of [0, 50%], while in the $η$ 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 Boström-Felbinger protocol, the insecurity upper bound of $η$ presented by Wójcik is pushed up in the this paper, that is, according to Wójcik's eavesdropping scheme, the Boström-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%.