In quantum direct communication an undetectable eavesdropper can always tellΨfromΦBell states in the message mode

Abstract

We show that in any quantum direct communication protocol that is based on $\ensuremath{\Psi}$ and $\ensuremath{\Phi}$ Bell states, an eavesdropper can always tell $\ensuremath{\Psi}$ from $\ensuremath{\Phi}$ states without altering the transmission in any way in the message mode. This renders all protocols that make use of only one $\ensuremath{\Psi}$ state and one $\ensuremath{\Phi}$ state completely insecure in the message mode. All four-Bell-state protocols require a revision and this might be of importance for new implementations of entanglement-based cryptographic protocols. The detection rate of an eavesdropper is 25$%$ per control transmission, i.e., a half of the rate in the two-state (ping-pong) protocol. An eavesdropper can detect control probes with certainty in the standard control transmission without a photon in the Alice-to-Bob's travel mode and with near certainty in a transmission with a fake photon in the travel mode. Resending of measured control photons via the travel mode would make an eavesdropper completely invisible.