  In this work, we prove that polar lattices, when tailored for lossy
compression, are quantization-good in the sense that their normalized second
moments approach $\frac{1}{2\pi e}$ as the dimension of lattices increases. It
has been predicted by Zamir et al. \cite{ZamirQZ96} that the Entropy Coded
Dithered Quantization (ECDQ) system using quantization-good lattices can
achieve the rate-distortion bound of i.i.d. Gaussian sources. In our previous
work \cite{LingQZ}, we established that polar lattices are indeed capable of
attaining the same objective. It is reasonable to conjecture that polar
lattices also demonstrate quantization goodness in the context of lossy
compression. This study confirms this hypothesis.
