  In this paper we develop the theory of quantum reverse hypercontractivity
inequalities and show how they can be derived from log-Sobolev inequalities.
Next we prove a generalization of the Stroock-Varopoulos inequality in the
non-commutative setting which allows us to derive quantum hypercontractivity
and reverse hypercontractivity inequalities solely from $2$-log-Sobolev and
$1$-log-Sobolev inequalities respectively. We then prove some
tensorization-type results providing us with tools to prove hypercontractivity
and reverse hypercontractivity not only for certain quantum superoperators but
also for their tensor powers. Finally as an application of these results, we
generalize a recent technique for proving strong converse bounds in information
theory via reverse hypercontractivity inequalities to the quantum setting. We
prove strong converse bounds for the problems of quantum hypothesis testing and
classical-quantum channel coding based on the quantum reverse
hypercontractivity inequalities that we derive.
