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A recent method to detect lower bonds to the classical capacity of quantum communication channels is applied for general damping channels in finite dimension    d  >  2   . The method compares the mutual information obtained by coding on the computational basis and on a Fourier basis, which can be obtained by just two local measurement settings and classical optimization. The results for large representative classes of different damping structures for high dimensional quantum systems are presented.

Bounding the Classical Capacity of Multilevel Damping Quantum Channels