A simple upper bound is derived to the difference in performance obtained from applying a given quanfizer to two different sources. This provides a bound on the performance loss or mismatch resulting when applying a quantizer designed for one source to another. The bound is in terms of a generalization of the Vasershtein distance between the source random variables and does not depend on the particular quantizer chosen. In particular, if two sources are sufficiently close in this sense, then any quantizer results in nearly identical performance on either source. Implications for optimal performance bounds are discussed and examples are given.
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Gray et al. (1975) studied this question.