Annales Henri Poincaré· 2026Q1
Strong Converse Exponent of Channel Interconversion
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Short summary
A new strong converse exponent for channel interconversion is derived, characterized by an optimization of Rényi channel capacities, extending previous work on simulating noisy channels.
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Key points
- The strong converse exponent for channel interconversion is characterized by optimizing the difference of Rényi channel capacities with Hölder dual parameters.
- This result extends to entanglement-assisted interconversion of classical-quantum channels, where the exponent depends on differences of sandwiched Rényi channel capacities.
- The converse bound is achieved using Hölder duality and the data processing inequality for Rényi divergences.
- Achievability is demonstrated through concatenated coding and simulation protocols that achieve exponentially small conversion errors and tolerate small input distribution variations.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In their seminal work, Bennett et al. [1] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding above this channel interconversion capacity, the exact strong converse exponent is characterized by a simple optimization involving the difference of the corresponding Rényi channel capacities with Hölder dual parameters. We further extend this result to the entanglement-assisted interconversion of classical–quantum channels, showing that the strong converse exponent is likewise determined by differences of sandwiched Rényi channel capacities. The converse bound is obtained by relaxing to non-signaling assisted codes and applying Hölder duality together with the data processing inequality for Rényi divergences. Achievability is proven by concatenating refined channel coding and simulation protocols that go beyond first-order capacities, attaining an exponentially small conversion error, remaining robust under small variations in the input distribution, and tolerating a sublinear gap between the conversion rates.
The authors' abstract, as published at the source. Annales Henri Poincaré, 2026 · DOI ↗
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Field: Electrical and Electronic Engineering
Electrical and Electronic EngineeringEngineering