Quantum Communication Using Coherent Rejection Sampling

Compression of a message up to the information it carries is key to many tasks involved in classical and quantum information theory. Schumacher [B. Schumacher, Phys. Rev. A 51, 2738 (1995)] provided one of the first quantum compression schemes and several more general schemes have been developed ever since [M. Horodecki, J. Oppenheim, and A. Winter, Commun. Math. Phys. 269, 107 (2007); I. Devetak and J. Yard, Phys. Rev. Lett. 100, 230501 (2008); A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc. R. Soc. A 465, 2537 (2009)]. However, the one-shot characterization of these quantum tasks is still under development, and often lacks a direct connection with analogous classical tasks. Here we show a new technique for the compression of quantum messages with the aid of entanglement. We devise a new tool that we call the convex split lemma, which is a coherent quantum analogue of the widely used rejection sampling procedure in classical communication protocols. As a consequence, we exhibit new explicit protocols with tight communication cost for quantum state merging, quantum state splitting, and quantum state redistribution (up to a certain optimization in the latter case). We also present a port-based teleportation scheme which uses a fewer number of ports in the presence of information about input.