I found going from the Choi-matrix of a quantum channel to the Choi-Kraus decomposition a bit difficult. I know that it follows from the eigen-decomposition of the Choi-matrix. But I struggle with both how this is done and how we derive the Kraus operators from this, both in the case of general channels and for specific channels.
I have tried to do this with the of "Amplitude damping channel" and end up with the Choi matrix $$ C_{N_{\gamma}}=\begin{bmatrix} 1 &0 &0 &\sqrt{1-\gamma}\\ 0&0&0&0\\ 0&0&\gamma&0\\\sqrt{1-\gamma}&0&0&1-\gamma \end{bmatrix} $$ But I don't know how to procede from here.
Any answers, general tips and where to read more would be appreciated.
