Quantum Achievability Proof via Collision Relative Entropy

This talk is about a simple framework for deriving one-shot achievable bounds for some problems in quantum information theory. This 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, some one-shot achievable bounds for the problems of communication over classical-quantum channels, quantum hypothesis testing, and classical data compression with quantum side information are derived. Using the method of information spectrum, I will argue that these one-shot achievable bounds give the asymptotic achievable rates of these problems even up to the second order.