  A central question in quantum information theory is to determine how well
lost information can be reconstructed. Crucially, the corresponding recovery
operation should perform well without knowing the information to be
reconstructed. In this work, we show that the quantum conditional mutual
information measures the performance of such recovery operations. More
precisely, we prove that the conditional mutual information $I(A:C|B)$ of a
tripartite quantum state $\rho_{ABC}$ can be bounded from below by its distance
to the closest recovered state $\mathcal{R}_{B \to BC}(\rho_{AB})$, where the
$C$-part is reconstructed from the $B$-part only and the recovery map
$\mathcal{R}_{B \to BC}$ merely depends on $\rho_{BC}$. One particular
application of this result implies the equivalence between two different
approaches to define topological order in quantum systems.
