  We provide a framework for one-shot quantum rate distortion coding, in which
the goal is to determine the minimum number of qubits required to compress
quantum information as a function of the probability that the distortion
incurred upon decompression exceeds some specified level. We obtain a one-shot
characterization of the minimum qubit compression size for an
entanglement-assisted quantum rate-distortion code in terms of the smooth
max-information, a quantity previously employed in the one-shot quantum reverse
Shannon theorem. Next, we show how this characterization converges to the known
expression for the entanglement-assisted quantum rate distortion function for
asymptotically many copies of a memoryless quantum information source. Finally,
we give a tight, finite blocklength characterization for the
entanglement-assisted minimum qubit compression size of a memoryless isotropic
qubit source subject to an average symbol-wise distortion constraint.
