A Strengthened Monotonicity Inequality of Quantum Relative Entropy: A Unifying Approach Via Renyi Relative Entropy

摘要

We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of -R,nyi relative entropy. We develop a unifying treatment toward 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 R,nyi relative entropy. The inequalities obtained, thus, extend 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.