A strengthened monotonicity inequality of quantum relative entropy: A unifying approach via Rényi relative entropy
arXiv:1403.5343 · doi:10.1007/s11005-016-0833-y
Abstract
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of $α$-Rényi relative entropy. We develop a unifying treatment towards the improvement of some quantum entropy inequalities. In particular, an emphasis is put on a lower bound of quantum conditional mutual information (QCMI) as it gives a Pinsker-like lower bound for the QCMI. We also give some improved entropy inequalities based on Rényi relative entropy. The inequalities obtained, thus, extends some well-known ones. We also obtain a condition under which a tripartite operator becomes a Markov state. As a by-product we provide some trace inequalities of operators, which are of independent interest.
17 pages, LaTeX, the title is changed: 'strengthened' in place of 'stronger'; final version, published in Lett. Math. Phys