Quantum f-divergences satisfy a local reverse Pinsker inequality implying that the asymptotic contraction rate of primitive channels is upper bounded by the SDPI constant of non-commutative χ²-divergences, with tightness under quantum detailed balance for Petz, Matsumoto, and Hirche-Tomamichel cases
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Tight Contraction Rates for Primitive Channels under Quantum $f$-Divergences
Quantum f-divergences satisfy a local reverse Pinsker inequality implying that the asymptotic contraction rate of primitive channels is upper bounded by the SDPI constant of non-commutative χ²-divergences, with tightness under quantum detailed balance for Petz, Matsumoto, and Hirche-Tomamichel cases