Consistent eavesdropping attack of two eavesdroppers on the ping-pong protocol with GHZ-triplets of qubits

Abstract

In this paper has been analyzed the eavesdropping attackof two eavesdroppers on the ping-pong protocol withthree-qubit entangled Greenberger – Horne – Zeilingerstates. The expression for probability of attack detectionby legitimate users at attack of two eavesdroppers dependingon probabilities of detection them attacks separatelyare obtained. It is shown that an increase in thenumber of attackers in the quantum channel leads to anincrease in the probability of detecting these attacks bylegitimate users. The expressions for the maximum eavesdroppers'amount of information during a consistentattack of two eavesdroppers on the ping-pong protocolwith GHZ-triplets are obtained. It is indicated that themaximum eavesdroppers' amount of information determinedby the same expression as in the case of oneeavesdropper's attack, only the expression for the probabilityof attack detection is changed. It is shown that theping-pong protocol with GHZ-triplets is vulnerable toeavesdropping attack of two eavesdroppers not morethan to one eavesdropper's attack. It is shown that resultsof paper could be extend to the ping-pong protocols withn-qubit GHZ-states at any n.