Compression of correlated quantum-classical sources, or: the price of ignorance

We resume the investigation of the problem of  independent local compression of correlated quantum sources,  the classical case of which is covered by the celebrated  Slepian-Wolf theorem. We focus specifically on quantum-classical (qc) sources,  for which one point of the rate region was previously  determined by Devetak and Winter. Whereas the Devetak- Winter point attains a rate-sum equal to the von Neumann  entropy of the joint source, here we show that the full rate region is much more complex due to the quantum nature of  one of the sources. In particular, we determine the full  rate region in the generic case, showing that all other  points in the achievable region have a rate sum strictly  larger than the joint entropy. We can interpret the difference  as the price paid for the quantum encoder being ignorant  of the classical side information. In the general case, we  give an achievable rate region, via protocols that are built  on the decoupling principle, state merging and state  redistribution. It is matched almost by a single-letter,  but still asymptotic, converse.