Non-coherent attack on the ping-pong protocol with completely entangled pairs of qutrits

The non-coherent attack on the ping-pong protocol with completely entangled pairs of three-dimensional quantum systems (qutrits) is analyzed. The expression for the amount of the eavesdropper’s information as functions of attack detection probability is derived. It is shown that the security of the ping-pong protocol with pairs of qutrits is higher than the security of the protocol with pairs of qubits. It is also shown that with the use by legitimate users in a control mode of two mutually unbiased measuring bases, the ping-pong protocol with pairs of qutrits possesses only asymptotic security, as well as the protocol with entangled qubits.