  We consider the reverse problem to the distinguishability of two quantum
channels, which we call the disguising problem. Given two quantum channels, the
goal here is to make the two channels identical by mixing with some other
channels with minimal mixing probabilities. This quantifies how much one
channel can disguise as the other. In addition, the possibility to trade off
between the two mixing probabilities allows one channel to be more preserved
(less mixed) at the expense of the other. We derive lower- and upper-bounds of
the trade-off curve and apply them to a few example channels. Optimal trade-off
is obtained in one example. We relate the disguising problem and the
distinguishability problem by showing the the former can lower and upper bound
the diamond norm. We also show that the disguising problem gives an upper bound
on the key generation rate in quantum cryptography.
