The bit error in quantum communication is mainly caused by eavesdropping and noise. However, most quantum communication protocols only take eavesdropping into consideration and ignore the result of noise, making the inaccuracy situations in detecting the eavesdropper. To analyze the security of the quantum E91 protocol presented by Ekert in collective-rotation noise channel, an excellent model of noise analysis is proposed. The increment of the qubits error rate (ber) is used to detect eavesdropping. In our analysis, eavesdropper (Eve) can maximally get about 50% of the key from the communication when the noise level approximates to 0.5. The results show that in the collective-rotation noise environment, E91 protocol is secure and the raw key is available just as we have knew and proved. We also presented a new idea in analyzing the protocol security in noise channel.
The bit error in quantum communication is mainly caused by eavesdropping and noise. However, most quantum communication protocols only take eavesdropping into consideration and ignore the result of noise, making the inaccuracy situations in detecting the eavesdropper. To analyze the security of the quantum E91 protocol presented by Ekert in collective-rotation noise channel, an excellent model of noise analysis is proposed. The increment of the qubits error rate (ber) is used to detect eavesdropping. In our analysis, eavesdropper (Eve) can maximally get about 50% of the key from the communication when the noise level approximates to 0.5. The results show that in the collective-rotation noise environment, E91 protocol is secure and the raw key is available just as we have knew and proved. We also presented a new idea in analyzing the protocol security in noise channel.
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.
Noise exists in the actual communication environment. It is necessary and significant to analyze the security of SAGR04 protocol in the noise environment. An excellent model of collective rotation noise analysis is introduced and the discussing of the security of SAGR04 protocol is based on the method of information theory. The eavesdropping can be detected for the increment of the qubit error rate and eavesdropper can maximally get about 50% of the keys. It can be concluded that the SAGR04 protocol, used as quantum key distribution, is secure.
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 Q 0 (M : (Q 0 , 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 is, the larger the error rate Q is. When the noise level 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 = Q 0 , eavesdropping information I > 1, which means that there exist eavesdroppers in the quantum channel, and the quantum channel will not be safe anymore.
Practical quantum key distribution (QKD) systems operate under noise, but security of most protocols have been analyzed under ideal noiseless scenarios. In this work, we investigated security performance of BB84 protocol under effect of collective rotation noise. Using theoretical quantum information frameworks, we analyzed key security parameters including quantum bit error rate (QBER), mutual information and secret key rate (SKR). Security of protocol is studied under various eavesdropping scenarios based on intercept and resend attacks. Our results show that collective rotation noise has a significant impact on the information shared between the two parties. Particularly, we extended prior treatments by suggesting a noise engineering strategy where we identified a non-zero noise range where information accessed by Eve is minimized while corresponding SKR degradation remains relatively small. This analysis provide insights into robustness of BB84 protocol under realistic noisy channels and may contribute towards development of more resilient QKD systems.
The security analysis of the Ekert 1991 (E91), Bennett 1992 (B92), six-state protocol, Scarani–Acín–Ribordy–Gisin 2004 (SARG04) quantum key distribution (QKD) protocols, and their variants have been studied in the presence of collective-rotation noise channels. However, besides the Bennett–Brassard 1984 (BB84) being the first proposed, extensively studied, and essential protocol, its security proof under collective-rotation noise is still missing. Thus, we aim to close this gap in the literature. Consequently, we investigate how collective-rotation noise channels affect the security of the BB84 protocol. Mainly, we study scenarios where the eavesdropper, Eve, conducts an intercept-resend attack on the transmitted photons sent via a quantum communication channel shared by Alice and Bob. Notably, we distinguish the impact of collective-rotation noise and that of the eavesdropper. To achieve this, we provide rigorous, yet straightforward numerical calculations. First, we derive a model for the collective-rotation noise for the BB84 protocol and parametrize the mutual information shared between Alice and Eve. This is followed by deriving the quantum bit error rate (QBER) for two intercept-resend attack scenarios. In particular, we demonstrate that, for small rotation angles, one can extract a secure secret key under a collective-rotation noise channel when there is no eavesdropping. We observe that noise induced by rotation of 0.35 radians of the prepared quantum state results in a QBER of 11%, which corresponds to the lower bound on the tolerable error rate for the BB84 QKD protocol against general attacks. Moreover, a rotational angle of 0.53 radians yields a 25% QBER, which corresponds to the error rate bound due to the intercept-resend attack. Finally, we conclude that the BB84 protocol is robust against intercept-resend attacks on collective-rotation noise channels when the rotation angle is varied arbitrarily within particular bounds.
Security of the quantum secure direct communication protocol (i.e., the C-S QSDC protocol) recently proposed by Cao and Song [Chin. Phys. Lett. 23 (2006) 290] is analyzed in the case of considerable quantum channel noise. The eavesdropping scheme is presented, which reveals that the C-S QSDC protocol is not secure if the quantum bit error rate (QBER) caused by quantum channel noise is higher than 4.17%. Our eavesdropping scheme induces about 4.17% QBER for those check qubits. However, such QBER can be hidden in the counterpart induced by the noisy quantum channel if the eavesdropper Eve replaces the original noisy channel by an ideal one. Furthermore, if the QBER induced by quantum channel noise is lower than 4.17%, then in the eavesdropping scheme Eve still can eavesdrop part of the secret messages by safely attacking a fraction of the transmitted qubits. Finally, an improvement on the C-S QSDC protocol is put forward.