  In this work, we analyze a number of noisy quantum channels on a family of
qudit states. The channels studied are the dit-flip noise, phase flip noise,
dit-phase flip noise, depolarizing noise, non-Markovian Amplitude Damping
Channel (ADC), dephasing noise, and depolarization noise. To gauge the effect
of noise, the fidelity between the original and the final states is studied.
The change of coherence under the action of noisy channels is also studied,
both analytically and numerically. Our approach is advantageous as it has an
explicit relation to the original approach to the multi-qubit hypergraph
states.
