Security of ping-pong protocol based on pairs of completely entangled qudits

Quantum secure direct communication protocols offer confidential transmission of classic information over quantum channel without prior key agreement. The ping-pong based protocols provide asymptotic security and detailed analysis of security level provided by each variant of the protocol is required. The paper presents a general method of calculation of the eavesdropped information as a function of the attack detection probability. The method is applied to the ping-pong protocol based on completely entangled pairs of qudits. The upper and lower bounds on the amount of the leaked information and eavesdropping detection probability are provided.