Quantum key distribution with several intercepts and resend attacks with partially non-orthogonal basis states

The effect of partially non-orthogonal basis states for several intercept and resend attacks of the Bennett–Brassard cryptographic protocol has been studied. The quantum error and the mutual information are computed for arbitrary angles η of the non-orthogonal basis states. It is found that the secure information depend strongly on the angle η, the probability of intercepts and resend attack and the number of eavesdropper. Besides, it is found that for any eavesdroppers number N ≥ 2, the protocol is more secured for (π/2) < η < (3π/2), while for N = 1, the protocol is more secured for η = π/2 or 3π/2 which correspond to the totally orthogonal basis states.