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Table 1 Properties of an BB84-like protocol under an arbitrary attack compared with properties of pp-like and LM05-like protocols under the attack presented in the paper

From: RETRACTED ARTICLE: Can Two-Way Direct Communication Protocols Be Considered Secure?

  BB84 pp LM05
Type Probabilistic Deterministic Deterministic
Mode(s) Message (MM) Message (MM) + control (CM) Message (MM) + control (CM)
Security QBER of MM QBER of CM QBER of CM
secure for QBER < 11% no/unknown no/unknown
disturbance 0≤D≤0.5 in MM D=0 in MM, 0≤D≤0.5 in CM D=0 in MM, 0≤D≤0.5 in CM
Critical disturbance D=0.11 Indeterminable — dependent on inherent QBER of the system Indeterminable — dependent on inherent QBER of the system
Mutual information I AB = 1 + D log2D +(1 − D)log2(1−D),I AE = −D log2D −(1 −D)log2(1 − D) I AB=1, 0≤I AE≤1 I AB=1, 0≤I AE≤1
Photon distance L 4L 2L
Transmittance \(\mathcal {T}\) \({\mathcal {T}}^{4}\) \({\mathcal {T}}^{2}\)
  1. 0≤I AE≤1 simply means that Eve might decide not to be in the line only a fraction of time. If she was in the line all the time, we would have I AE=1