Correlated source coding with quantum side information at two decoders

In this paper, we introduce an information-theoretic task that we refer to as correlated sources coding where decoders possess complementary quantum side information. We present the optimal rates for lossless correlated sources coding with both complementary and less noisy quantum side information. We also generalize quantum Sgarro's coding and correlated sources coding with complementary quantum side information to scenarios with distortion.