2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141257Using a generalization of the invariant information introduced by Brukner and Zeilinger [Phys. Rev. Lett. \textbf{83}, 3354 (1999)] to high-dimensional systems, we introduce a complementarity relation between the local and nonlocal information for $d\times d$ systems under the isolated environment, where $d$ is prime or the power of prime. We also analyze the dynamics of the local information in the decoherence process.4 pages, 2 figuresQuantum Physicstext