Narrow Results

The effect of several eavesdroppers intercept-resend attacks on the quantum error and mutual information between honest parties of a quantum channel chain is investigated within the BB84 (Bennett and Brassard, 1984). The quantum error and the mutual information are computed for arbitrary number of attacks. It is found that the quantum error and the secured–no secured transition depend strongly on the number N of eavesdroppers and their probabilities of intercepting attacks. For N = 3, numerical calculations show that the quantum error exhibits three kinds of different behaviors as a function of the probability of attack ω₁ of the first eavesdropper namely: (i) the quantum error remains constant for sufficiently small ω₁, (ii) exhibits a plateau for intermediate values of ω₁, (iii) increases, passes through a maximum and decreases when increasing ω₁. However, depending on the probabilities of attack, phase diagrams present several kinds of topologies, in good agreement with the quantum error behavior. Moreover, in the particular case where all eavesdroppers intercept with identical probabilities ω, the quantum error increases as a nonlinear function with the number of eavesdroppers before reaching an upper limit of ≈ 0.475 for sufficiently large N. Besides, it is shown that the secured–no secured transition occurs under the effect of the number of eavesdroppers.

In this work, an estimation of the key rate of measurement-device-independent quantum key distribution (MDI-QKD) protocol in free space was performed. The examined free space links included satellite-earth downlink, uplink and intersatellite link. Various attenuation effects were considered such as diffraction, atmosphere, turbulence and the efficiency of the detection system. Two cases were tested: asymptotic case with infinite number of decoy states and one-decoy state case. The estimated key rate showed the possibility of applying MDI-QKD in earth-satellite and intersatellite links, offering longer single link distance to be covered.