On the whiteness of high resolution quantization errors

A common belief in quantization theory says that the quantization noise process resulting from uniform scalar quantization of a correlated discrete time process tends to be white in the limit of small distortion ("high resolution"). We show that the quantization errors resulting from independent non-uniform, vector quantizations of dependent real random vectors become asymptotically uncorrelated if the joint Fisher information under translation of the two vectors is finite and the quantization cells shrink uniformly as the distortion tends to zero.