# What is a covariant quantum channel?

A novice to this topic, I am trying to understand the notion of (irreducible) Covariant Quantum Channels. This article provides a definition that is not very "physical". My question:

1. What is the intuition behind the notion of covariant quantum channels?
2. Is the Generalized Amplitude Damping channel an example of (irreducible) Covariant Quantum Channel?

Let's start with the mathematical definition quoted in the paper: for a quantum channel $$\Phi(\rho)$$ acting on density operators and a set of unitary operators $$U$$ belonging to some group, the equality $$\Phi(U \rho U^\dagger)=U \Phi(\rho)U^\dagger$$ implies that the channel is covariant with respect to the group. For a simple unitary channel like $$\Phi(\rho)=V\rho V^\dagger$$, the covariance property is equivalent to finding a group of unitaries that commute with $$V$$ ($$UV-VU=0$$ for all $$U$$ in the group).