Abstract
The data processing inequality states that the quantum relative entropy
between two states $\rho$ and $\sigma$ can never increase by applying the same
quantum channel $N$ to both states. This inequality can be
strengthened with a remainder term in the form of a distance between $\rho$ and
the closest recovered state $(R N)(\rho)$, where
$R$ is a recovery map with the property that $= (R
N)(\sigma)$. We show the existence of an explicit recovery map
that is universal in the sense that it depends only on $\sigma$ and the quantum
channel $N$ to be reversed. This result gives an alternate,
information-theoretic characterization of the conditions for approximate
quantum error correction.
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