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
On the strong converses for the quantum channel capacity theorems
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abstract
A unified approach to prove the converses for the quantum channel capacity theorems is presented. These converses include the strong converse theorems for classical or quantum information transfer with error exponents and novel explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz strong converse for the classical channel capacity theorems. We provide a new proof for the error exponents for the classical information transfer. A long standing problem in quantum information theory has been to find out the strong converse for the channel capacity theorem when quantum information is sent across the channel. We give the quantum error exponent thereby giving a one-shot exponential upper bound on the fidelity. We then apply our results to show that the strong converse holds for the quantum information transfer across an erasure channel for maximally entangled channel inputs.
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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
- Tighter Information-Theoretic Generalization Bounds via a Novel Class of Change of Measure Inequalities