the quality of other electronic properties!

The reason for the above-mentioned mobility/quality dichotomy is rather obvious to state, but not easy to quantify. Both mobility and quality (e.g., the measured activation gap for a specific FQHE state or some other specified electronic property) depend on the full disorder distribution affecting the system which is in general both unknown and complex, and depends also on the sample carrier density in a complicated manner. The disorder distribution is characterized by many independent parameters, and therefore, all physical properties of the system, being unique functionals of the disorder distribution, are independent of each other. In particular, the dc conductivity $\sigma$, which determines the density-dependent mobility $\mu = \sigma/ne$ where $n$ is the 2D carrier density (and $e$ the magnitude of electron charge), is determined by essentially an integral over the second moment of the disorder distribution whereas other physical properties (i.e., the quality, although there could, in principle, be many independent definitions of sample quality depending on independent experimental measurements of interest) could be determined by other functionals of the disorder distribution. Thus, for any realistic disorder distribution, we do not expect any unique relationship between mobility and quality, and it should be 