Iterates of the Petz recovery map composed with a trace-preserving map converge in norm to a projection onto the set of recoverable states on von Neumann algebras, with an additional decomposition theorem for normal states.
Petz,Sufficient subalgebras and the relative entropy of states of a von Neumann algebra, Comm
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Recoverable states on von-Neumann algebras
Iterates of the Petz recovery map composed with a trace-preserving map converge in norm to a projection onto the set of recoverable states on von Neumann algebras, with an additional decomposition theorem for normal states.