Invariant information and complementarity in high-dimensional states

TL;DR

This paper generalizes invariant information to high-dimensional quantum systems, establishing a complementarity relation between local and nonlocal information and analyzing their dynamics under decoherence.

Contribution

It introduces a new complementarity relation for high-dimensional systems based on generalized invariant information, extending previous concepts to prime and prime power dimensions.

Findings

Established a complementarity relation between local and nonlocal information.

Analyzed the dynamics of local information during decoherence.

Extended invariant information concepts to high-dimensional quantum systems.

Abstract

Using 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.