Compactness Criterion for Families of Quantum Operations in the Strong Convergence Topology and Its Applications

A revised version of the compactness criterion for families of quantum operations in the strong convergence topology obtained in [1] is presented, along with a more detailed proof and the examples showing the necessity of this revision. Several criteria for the existence of limit points of a sequence of quantum operations w.r.t. the strong convergence are obtained and discussed. Applications in different areas of quantum information theory are described.