  A quantized metric space is a matrix order unit space equipped with an
operator space version of Rieffel's Lip-norm. We develop for quantized metric
spaces an operator space version of quantum Gromov-Hausdorff distance. We show
that two quantized metric spaces are completely isometric if and only if their
quantized Gromov-Hausdorff distance is zero. We establish a completeness
theorem. As applications, we show that a quantized metric space with 1-exact
underlying matrix order unit space is a limit of matrix algebras with respect
to quantized Gromov-Hausdorff distance, and that matrix algebras converge
naturally to the sphere for quantized Gromov-Hausdorff distance.
