Abstract: This work establishes connection between channel simulation and coded source compression. First, we consider classical source coding with quantum side-information where the quantum side-information is observed by a helper and sent to the decoder via a classical channel. We derive a single-letter characterization of the achievable rate region for this problem. The direct part of our result is proved via the measurement compression theory by Winter, a quantum to classical channel simulation. Our result reveals that a helpers scheme that separately conducts a measurement and a compression is suboptimal, and the measurement compression is fundamentally needed to achieve the optimal rate region. We then study coded source compression in the fully quantum regime. We characterise the quantum resources involved in this problem, and derive a single-letter expression of the achievable rate region when entanglement assistance is available. The direct coding proof is based on a combination of two fundamental protocols, namely the quantum state merging protocol and the quantum reverse Shannon theorem. Our work hence resolves coded source compression in the quantum regime.

Date: 25 November 2015