  In this work we study the problem of communication over the quantum wiretap
channel. For this channel there are three parties Alice (sender), Bob
(legitimate receiver) and Eve (eavesdropper). We obtain upper and lower bounds
on the amount of information Alice can communicate to Bob such that Eve gets to
know as little information as possible about the transmitted messages. Our
bounds are in terms of quantum hypothesis testing divergence and smooth max
quantum relative entropy. To obtain our result we prove a one-shot version of
the quantum covering lemma along with operator Chernoff bound for non-square
matrices.
