AB  - © 2017 IEEE. A Markov chain is a tripartite quantum state ?ABC where there exists a recovery map RB?BC such that ?ABC = RB?BC(?AB). More generally, an approximate Markov chain ?ABC is a state whose distance to the closest recovered state RB?BC(?AB) is small. Recently it has been shown that this distance can be bounded from above by the conditional mutual information I(A: C|B)? of the state. We improve on this connection by deriving the first bound that is tight in the commutative case and features an explicit recovery map that only depends on the reduced state pBC. The key tool in our proof is a multivariate extension of the Golden-Thompson inequality, which allows us to extend logarithmic trace inequalities from two to arbitrarily many matrices.
AU  - Sutter, D
AU  - Berta, M
AU  - Tomamichel, M
DA  - 2017/08/09
DO  - 10.1109/ISIT.2017.8006877
EP  - 1992
JO  - IEEE International Symposium on Information Theory - Proceedings
PY  - 2017/08/09
SP  - 1988
TI  - Quantum Markov chains and logarithmic trace inequalities
Y1  - 2017/08/09
Y2  - 2026/07/23
ER  -