Entanglement-Assisted Quantum Data Compression

Ask how the quantum compression of ensembles of pure states is affected by the availability of entanglement, and in settings where the encoder has access to side information. We find the optimal asymptotic quantum rate and the optimal tradeoff (rate region) of quantum and entanglement rates. It turns out that the amount by which the quantum rate beats the Schumacher limit, the entropy of the source, is precisely half the entropy of classical information that can be extracted from the source and side information states without disturbing them at all ("reversible extraction of classical information"). In the special case that the encoder has no side information, or that she has access to the identity of the states, this problem reduces to the known settings of blind and visible Schumacher compression, respectively, albeit here additionally with entanglement assistance. We comment on connections to previously studied and further rate tradeoffs when also classical information is considered.