A novel quantum secure direct communication protocol based on four-particle genuine entangled state and quantum dense coding is proposed. In this protocol, the four-particle genuine entangled state is used to detect eavesdroppers, and quantum dense coding is used to encode the message. Finally, the security of the proposed protocol is discussed. During the security analysis, the method of entropy theory is introduced, and two detection strategies are compared quantitatively by comparing the relationship between the maximal information that the eavesdroppers (Eve) can obtain, and the probability of being detected. Through the analysis we can state that our scheme is feasible and secure.

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Most of quantum cryptography protocols are designed under the ideal conditions without considering the impact of noise in actual communication; thus they may result in that the confidential information cannot be transmitted to the receiver accurately or eavesdroppers can steal the confidential information by mixing in noise. Therefore, analyzing the security of quantum cryptography protocols under noise conditions is of great significance. For the purpose of analyzing the security of quantum BB84 protocol in collective-rotation noise, firstly this paper introduces the quantum BB84 protocol, and considers the influence of environmental noise on it. An explanation should be stated that in a noise environment, the effects of noise and eavesdropping cannot be distinguished between each other. So the mechanism for which the error bit is simply used as the criterion to judge whether there exists eavesdropping in the BB84 protocol, cannot be used in the noise environment. The mechanism to judge whether there exists eavesdropping in quantum noise channel needs to be modified and improved for protecting the information. An initial qubit error rate can be set according to the noisy quantum channel. If the qubit error rate of the quantum communication channel is larger than that, it can be determined that the quantum channel is not secure and exists eavesdropping, no matter what the reason is. And on this basis, the collective-rotation noise model will be established in quantum channel by using the particle deflection model and distinguish the noise from the eavesdropping in quantum channel quantitatively, and the relationship of the amount of information that eavesdroppers can steal, the quantum bits error rate and the noise level will be analyzed by using the von Neumann entropy. Finally, the noise critical point will be calculated by using the collective noise model and the relationship between the amount of information that eavesdroppers can steal, at the quantum bits error rate, and the noise level. Through the analysis, we can know that in the existing noise level, the most of the eavesdropping can steal 25% of the key from the communication. However, the Eve's eavesdropping behavior will be detected, so that Alice and Bob will give up the current consultation key, and restart the key negotiation. This result shows that the quantum BB84 protocol is safe and secure in the collective-rotation noise channel. The research results of this paper will enrich the theory of quantum cryptography, and the innovation of security detection methods in quantum cryptographic protocols will help promote the process of practical quantum cryptography.

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.