  Optimally encoding classical information in a quantum system is one of the
oldest and most fundamental challenges of quantum information theory. Holevo's
bound places a hard upper limit on such encodings, while the
Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many
classical messages can be "packed" into a given quantum system. In this
article, we use Sen's recent quantum joint typicality results to prove a
one-shot multiparty quantum packing lemma generalizing the HSW theorem. The
lemma is designed to be easily applicable in many network communication
scenarios. As an illustration, we use it to straightforwardly obtain quantum
generalizations of well-known classical coding schemes for the relay channel:
multihop, coherent multihop, decode-forward, and partial decode-forward. We
provide both finite blocklength and asymptotic results, the latter matching
existing classical formulas. Given the key role of the classical packing lemma
in network information theory, our packing lemma should help open the field to
direct quantum generalization.
