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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.
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Jon Tyson, private communication. Since the discrete Weyl-Heisenberg group is an orthonormal basis for d × d d\times d matrices, it is easy to check that a change of basis has the same property
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