I have heard about the diamond norm, and from what I understood it is a "nice" tool to quantify quality of quantum gates in the NISQ era. I would like to know a little more before going in detail in the litterature.
My question are the following:
Why is it considered as a good tool to quantify quality of quantum gates? Why this tool and not another one?
What are the nice properties this tool has? I have seen in Is the diamond norm subadditive under composition? that it is subbaditive which make the tool useful to bound the diamond norm of a full algorithm given the diamond norm of each gate. Are there other some useful properties? I guess this question will be related somehow to the previous one. I tried to find this information in literature, but unfortunately all papers I read just give the definition and the diamond norm and a way to compute it numerically.