  When there exists a malicious attacker in the network, we need to be careful
of eavesdropping and contamination. This problem is crucial for network
communication when the network is realized by a partially trusted relay of
quantum key distribution. We discuss the asymptotic rate in a linear network
with the secrecy and robustness conditions when the above type of attacker
exists. Also, under the same setting, we discuss the asymptotic rate in a
linear network when we impose the secrecy condition alone. Then, we apply these
results to the network composed of a partially trusted relay of quantum key
distribution, which enables us to realize secure long-distance communication
via short-distance quantum key distribution.
