2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89020We review the role of product bases in quantum information theory. We prove two conjectures which were made in DiVincenzo et al., quant-ph/9908070, namely the existence of two sets of bipartite unextendible product bases, in arbitrary dimensions, which are based on a tile construction. We pose some questions related to complete product bases.9 pages, 4 figures; submitted to the Proceedings of the XIII International Congress on Mathematical PhysicsQuantum Physicstext