  In this paper, we provide a simple framework for deriving one-shot achievable
bounds for some problems in quantum information theory. Our framework is based
on the joint convexity of the exponential of the collision relative entropy,
and is a (partial) quantum generalization of the technique of Yassaee et al.
(2013) from classical information theory. Based on this framework, we derive
one-shot achievable bounds for the problems of communication over
classical-quantum channels, quantum hypothesis testing, and classical data
compression with quantum side information. We argue that our one-shot
achievable bounds are strong enough to give the asymptotic achievable rates of
these problems even up to the second order.
