Strong converse exponent of channel interconversion

2025-09-18

AI Summary

This work addresses the strong converse exponent problem for channel interconversion beyond capacity limits—specifically, characterizing the exponential decay rate of the error probability when the coding rate exceeds the channel conversion capacity, and extending this to entanglement-assisted classical-quantum channels. Methodologically, it innovatively couples Rényi channel capacity differences with Hölder conjugate parameters, integrating no-signaling assistance relaxation, the data-processing inequality for Rényi divergences, and cascaded simulation protocols. This yields the first tight strong converse exponent bound. The results apply broadly to both classical and quantum channel interconversion under shared randomness or entanglement assistance, achieving exponentially small conversion error. Moreover, the bound is robust against input distribution perturbations and permits sublinear deviations in the conversion rate.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Information Theory
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Assisted, interactive, and conversational search
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] 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.

Problem

• Characterizing strong converse exponent for channel interconversion
• Extending results to entanglement-assisted classical-quantum channels
• Establishing exact exponent through Rényi capacity optimization

Innovation

• Rényi capacities optimization for strong converse
• Non-signaling codes with Hölder duality application
• Refined channel coding simulation protocols