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

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 presence collective-rotation noise channels. However, besides Bennett–Brassard 1984 (BB84) being first proposed, extensively studied, essential its proof under is still missing. Thus, we aim to close this gap literature. Consequently, investigate how channels affect BB84 protocol. Mainly, study scenarios where eavesdropper, Eve, conducts an intercept-resend attack on transmitted photons sent via a communication channel shared by Alice Bob. Notably, distinguish impact that eavesdropper. To achieve this, provide rigorous, yet straightforward numerical calculations. First, derive model for protocol parametrize mutual information between Eve. This followed deriving bit error rate (QBER) two scenarios. In particular, demonstrate that, small rotation angles, one can extract secure secret when there no eavesdropping. We observe induced 0.35 radians prepared state results QBER 11%, which corresponds lower bound tolerable QKD against general attacks. Moreover, rotational angle 0.53 yields 25% QBER, due attack. Finally, conclude robust attacks varied arbitrarily within particular bounds.