2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69402We introduce a new quantum Gromov-Hausdorff distance between C*-algebraic compact quantum metric spaces. Because it is able to distinguish algebraic structures, this new distance fixes a weakness of Rieffel's quantum distance. We show that this new quantum distance has properties analogous to the basic properties of the classical Gromov-Hausdorff distance, and we give criteria for when a parameterized family of C*-algebraic compact quantum metric spaces is continuous with respect to this new distance.27 pages. Small modificationsOperator AlgebrasQuantum AlgebraPrimary 46L87; Secondary 53C23, 58B34text