Remarks on on Kim's Strong Subadditivity Matrix Inequality: Extensions and Equality Conditions

Abstract

We describe recent work of Kim in arXiv:1210.5190 to show that operator convex functions associated with quasi-entropies can be used to prove a large class of new matrix inequalities in the tri-partite and bi-partite setting by taking a judiciously chosen partial trace over all but one of the spaces. We give some additional examples in both settings. Furthermore, we observe that the equality conditions for all the new inequalities are essentially the same as those for strong subadditivity.

Kim's remarkable strengthening in arXiv:1210.5190 of strong subadditvity of quantum entropy to a matrix inequality was posted very close to the 40th anniversary of the actual proof of SSA

References in corpus (3)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
• Operator extension of strong subadditivity of entropy

Cited by in corpus (7)

• A lower bound of quantum conditional mutual information
• On quantum quasi-relative entropy
• A strengthened monotonicity inequality of quantum relative entropy: A unifying approach via Rényi relative entropy
• A new operator extension of strong subadditivity of quantum entropy
• On some entropy inequalities
• Recoverability from direct quantum correlations
• Yet Another Proof of the Joint Convexity of Relative Entropy