Title: A Quantum Multiparty Packing Lemma and the Relay Channel

Abstract: Encoding classical information into a quantum system is one of the most fundamental questions of quantum information theory. Classic results in this area include the Holevo bound and the Holevo-Schumacher-Westmoreland theorem. The setup can be imagined as a black box which takes a random variable encoding the information as input and outputs a quantum state. Under appropriate conditions, the information can be retrieved via a decoding quantum measurement. In this work, we prove that decoders for different black boxes can be combined into one simultaneous decoder for a black box that takes as input the joint random variable across all the black boxes. This resolves a long-standing open problem in quantum network information theory known as simultaneous decoding and was made possible by Pranab Sen's recent quantum joint typicality lemma. We demonstrate the use of our results for the quantum relay channel, a possible communication model for quantum repeaters.