English

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

Quantum Physics 2015-06-12 v1 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.1211.0049,
  title  = {Remarks on on Kim's Strong Subadditivity Matrix Inequality: Extensions and Equality Conditions},
  author = {Mary Beth Ruskai},
  journal= {arXiv preprint arXiv:1211.0049},
  year   = {2015}
}

Comments

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