Effective Noise Estimation for Secure Quantum Direct Communication over Imperfect Channels

In quantum communication actions of an eavesdropper are perceived by legitimate parties as some additional noise so correct estimation of the noise level is vital element of any protocol. The Ping-Pong protocol, one of the most widely recognized applications of entanglement for quantum direct communication, has been formulated with perfect quantum channels in mind and noise estimation is not addressed in its design. The control mode of the protocol's seminal version cannot be used for this purpose as it is insensitive to phase flips of a signal qubit which at the same time contribute to errors observed in message mode. As a result, failures of the control mode are not related to errors in the message mode and, in consequence, in noisy environments it is possible to mount undetectable attacks which provide non-zero information gain to the eavesdropper. The control mode improvement which permits correct estimation of errors occurring in message mode is proposed and analyzed. The proposed modification explores the fact that local measurements in mutually unbiased bases reveal the coherence loss between distant components of the entangled system.