The Security Analysis of Two-Step Quantum Direct Communication Protocol in Collective-Rotation Noise Channel

To analyze the security of two-step quantum direct communication protocol (QDCP) by using Einstein–Podolsky–Rosen pair proposed by Deng et al. Phys. Rev. A 68 (2003) 042317 in collective-rotation noise channel, an excellent model of noise analysis is proposed. In the security analysis, the method of the entropy theory is introduced, and is compared with QDCP, an error rate point Q₀(M:(Q₀,1.0)) is given. In different noise levels, if Eve wants to obtain the same amount of information, the error rate Q is distinguishable. The larger the noise level ε is, the larger the error rate Q is. When the noise level ε is lower than 11%, the high error rate is 0.153 without eavesdropping. Lastly, the security of the proposed protocol is discussed. It turns out that the quantum channel will be safe when Q<0.153. Similarly, if error rate Q>0.153=Q₀, eavesdropping information I>1, which means that there exist eavesdroppers in the quantum channel, and the quantum channel will not be safe anymore.