Achievability bounds on quantum state redistribution using convex split and position based decoding

Quantum state redistribution is a fundamental quantum information theoretic primitive that captures a generic quantum communication scenario. In this work, we study the problem of entanglement assisted quantum state redistribution in one-shot setting and provide a new achievability result on the quantum communication required. Our bounds are in terms of max relative entropy and Rényi relative entropy of order 2. We show that our result is upper bounded by the result obtained in Berta, Christandl, Touchette (2016) (which is in terms of smooth conditional max and min entropies). We use the techniques of convex split and position based decoding (through pretty good measurement) to arrive at our result. Furthermore, in order to clarify the connection between our result and other recent results that use convex split and position based decoding, we prove a new relation between the hypothesis testing relative entropy and Rényi relative entropy of order 2.