Source coding with quantum side information at several decoders

We consider the task of the classical source coding with quantum side information at several decoders. This is a quantum generalization of classical Sgarro’s three correlated information sources. We focus on classical–quantum sources, which involve the classical coding part, using the quantum part as side information at the decoder. We consider two models: non-entangled and entangled side information. To obtain optimal coding rate, we develop a quantum version of maximal simultaneous codes. The achievable rate is found to be determined by the maximally quantum conditional entropy between the classical source and side information. In particular, our result shows that the more the size of the quantum part, the smaller the coding rate.