Security of Bennett–Brassard 1984 Quantum-Key Distribution under a Collective-Rotation Noise Channel

Abstract

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.

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“…The QBER comparison of BB84 and KMB09 under the channel noise effect is further illustrated in Table II. For an angle of π/4 we observe from Table II that the QBER obtained for our system model is similar to that obtained in [48] which uses BB84 QKD protocol over a similar type of noise channel model i.e. the collective-rotation noise channel.…”

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“…In particular, after quantum electrodynamics was established, it was confirmed that photons are medium particles for the transmission of electromagnetic information. Photons are often used for quantum information transmission [1][2][3][4] because of their excellent properties of easy generation and manipulation and their ability to transmit over long distances through free-space or fiber channels [5]. Therefore, It is very important and meaningful to study various applications in electronic commerce based on quantum mechanics using photons as information carriers.…”

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“…Therefore, the role of photons in quantum communication is of great significance. Quantum communication includes various protocols and applications, such as quantum key distribution (QKD) [2][3][4][5][6][7][8][9][10][11][12], quantum secret sharing (QSS) [13][14][15], quantum key agreement (QKA) [16][17][18], quantum private query (QPQ) [19][20][21], quantum multi-party computation (QMC) [22][23][24][25][26], and so on.…”