Invariant information and complementarity in high-dimensional states

Using a generalization of the invariant information introduced by Brukner and Zeilinger [Phys. Rev. Lett. 83, 3354 (1999)] to high-dimensional systems, we introduce a complementarity relation between the local and nonlocal information for dxd systems under an isolated environment, where d is prime or a power of a prime number. We also analyze the dynamics of the local information in the decoherence process