  We point out that labeled causets have a much simpler structure than
unlabeled causets. For example, labeled causets can be uniquely specified by a
sequence of integers. Moreover, each labeled causet processes a unique
predecessor and hence has a unique history. Our main result shows that an
arbitrary quantum sequential growth process (QSGP) on the set of labeled
causets "compresses" in a natural way onto a QSGP on the set of unlabeled
causets. The price we have to pay is that this procedure causes an "explosion"
of values due to multiplicities. We also observe that this procedure is not
reversible. This indicates that although many QSGPs on the set of unlabeled
causets can be constructed using this method, not all can, so it is not
completely general. We close by showing that a natural metric can be defined on
labeled and unlabeled causets and on their paths.
