  We discuss the Ping-Pong protocol which was proposed by Bostroem and
Felbinger. We derive a simple trade-off inequality between distinguishability
of messages for Eve and detectability of Eve for legitimate users. Our
inequality holds for arbitrary initial states. That is, even if Eve prepares an
initial state, she cannot distinguish messages without being detected. We show
that the same inequality holds also on another protocol in which Alice and Bob
use one-way quantum communication channel twice.
