Universal recovery maps and approximate sufficiency of quantum relative entropy
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.07127
- arXiv:
- arXiv:1509.07127
- Bibcode:
- 2015arXiv150907127J
- Keywords:
-
- Quantum Physics;
- Computer Science - Information Theory;
- Mathematical Physics
- E-Print:
- v3: 24 pages, 1 figure, final version published in Annales Henri Poincar\'e