A New Distributed Source Coding Problem Related to the Classical-Quantum Slepian–Wolf Problem

Suppose there are two correlated sources, one producing classical data and the other producing mixed states with commuting density operators. We combine the two sources into one and call it a classical-quantum source. In this paper, we consider the problem of distributed compression of the classical-quantum source. This is a special case of the classical-quantum Slepian-Wolf problem addressed by Devetak and Winter [1]. Suppose Alice (resp. Bob) receives classical (resp. quantum) data from the classical-quantum source. Alice and Bob, who cannot communicate with each other, want to send their received data to Charlie at the minimum communication cost. We consider two scenarios, the blind and visible scenarios, for Bob's quantum data compression. We formulate our problem in terms of classical information theory and then using some results in classical information theory, we show partial results on the achievable rate region for asymptotically lossless distributed compression of the classical-quantum source in the blind and visible scenarios.