Editing Quantum operation (section)

===Remarks===
These results can be also derived from [[Choi's theorem on completely positive maps]], characterizing a completely positive finite-dimensional map by a unique Hermitian-positive density operator ([[Choi matrix]]) with respect to the trace. Among all possible Kraus representations of a given [[quantum channel|channel]], there exists a canonical form distinguished by the orthogonality relation of Kraus operators, <math>\operatorname{Tr} A^\dagger_i A_j \sim \delta_{ij} </math>. Such canonical set of orthogonal Kraus operators can be obtained by diagonalising the corresponding Choi matrix and reshaping its eigenvectors into square matrices.

There also exists an infinite-dimensional algebraic generalization of Choi's theorem, known as "Belavkin's Radon-Nikodym theorem for completely positive maps", which defines a density operator as a "Radon–Nikodym derivative" of a [[quantum channel]] with respect to a dominating completely positive map (reference channel). It is used for defining the relative fidelities and mutual informations for quantum channels.