There is a very important theorem in mathematics, called Kraus’ Representation Theorem, which states that maps of the form in Eq. (6.10) with the restriction that \(\sum_{k} A_{k}^{\dagger} A_{k}=\mat...There is a very important theorem in mathematics, called Kraus’ Representation Theorem, which states that maps of the form in Eq. (6.10) with the restriction that \(\sum_{k} A_{k}^{\dagger} A_{k}=\mathbb{I}\) is a completely positive map, and moreover, that any completely positive map can be expressed in this form.
