%0 Generic %1 junge2015universal %A Junge, Marius %A Renner, Renato %A Sutter, David %A Wilde, Mark M. %A Winter, Andreas %D 2015 %K information quantum %R 10.1007/s00023-018-0716-0 %T Universal recovery maps and approximate sufficiency of quantum relative entropy %U http://arxiv.org/abs/1509.07127 %X 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.

@misc{junge2015universal, 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 $\mathcal{N}$ 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 $(\mathcal{R} \circ \mathcal{N})(\rho)$, where $\mathcal{R}$ is a recovery map with the property that $\sigma = (\mathcal{R} \circ \mathcal{N})(\sigma)$. 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 $\mathcal{N}$ to be reversed. This result gives an alternate, information-theoretic characterization of the conditions for approximate quantum error correction.}, added-at = {2023-08-12T22:03:47.000+0200}, author = {Junge, Marius and Renner, Renato and Sutter, David and Wilde, Mark M. and Winter, Andreas}, biburl = {https://www.bibsonomy.org/bibtex/2909e8922b8f433728dab3a4cb66f3dac/gzhou}, description = {Universal recovery maps and approximate sufficiency of quantum relative entropy}, doi = {10.1007/s00023-018-0716-0}, interhash = {772553b53ae6a2ef2f5d913fd6dd62d6}, intrahash = {909e8922b8f433728dab3a4cb66f3dac}, keywords = {information quantum}, note = {cite arxiv:1509.07127Comment: v3: 24 pages, 1 figure, final version published in Annales Henri Poincar\'e}, timestamp = {2023-08-12T22:03:47.000+0200}, title = {Universal recovery maps and approximate sufficiency of quantum relative entropy}, url = {http://arxiv.org/abs/1509.07127}, year = 2015 }