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A revised version of the compactness criterion for families of quantumoperations in the strong convergence topology (obtained previously) ispresented, along with a more detailed proof and the examples showing thenecessity of this revision.  Several criteria for the existence of a limit point of a sequence of quantumoperations w.r.t. the strong convergence are obtained and discussed.  Applications in different areas of quantum information theory are described.

Compactness criterion for families of quantum operations in the strong convergence topology and its applications