A generalized quantum Slepian-Wolf

In this work we consider a quantum generalization of the task considered by Slepian and Wolf [1973] regarding distributed source compression. In our task Alice, Bob, Charlie and Reference share a joint pure state. Alice and Bob wish to send a part of their respective systems to Charlie without collaborating with each other. We give achievability bounds for this task in the one-shot setting and provide the asymptotic and i.i.d. analysis in the case when there is no side information with Charlie. Our result implies the result of Abeyesinghe, Devetak, Hayden and Winter [2009] who studied a special case of this problem. As another special case wherein Bob holds trivial registers, we recover the result of Devetak and Yard [2008] regarding quantum state redistribution.