If a convex function is operator convex along every line, its epigraph's natural log-barrier is self-concordant, giving optimal barriers for sandwiched Rényi entropies.
Quantum hypothesis testing and the operational interpretation of the quantum R´ enyi relative entropies,
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Operator convexity along lines, self-concordance, and sandwiched R\'enyi entropies
If a convex function is operator convex along every line, its epigraph's natural log-barrier is self-concordant, giving optimal barriers for sandwiched Rényi entropies.