Quantum Rate-Distortion Theory for I.I.D. Sources

We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an unrestricted classical side channel, we find the exact quantum rate-distortion function for a source of isotropic qubits. An upper bound we believe to be exact is found in the case of biased sources. We establish that in this scenario optimal rate-distortion codes produce no entropy exchange with the environment of any individual qubit.