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

One-Shot Private Classical Capacity of Quantum Wiretap Channel: Based on one-shot quantum covering lemma