Quantum Reverse Shannon Theorem Simplified

2025-10-06

AI Summary

This work addresses the one-shot resource cost of quantum channel simulation under the assumption of freely shared entanglement. To overcome limitations of existing approaches—namely, reliance on post-selection, technical complexity, and loose bounds—we introduce an additive upper bound based on the sandwiched Rényi mutual information, yielding the first post-selection-free proof with greater conceptual simplicity and technical directness. Building upon this, we further integrate smooth max-mutual information with the quantum information spectrum method to derive a non-asymptotic, universal bound. Our results substantially improve the one-shot quantum reverse Shannon theorem’s resource bounds, unify and simplify multiple prior frameworks, and enhance theoretical precision, applicability across channel classes, and interpretability of the underlying resource trade-offs.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We revisit the quantum reverse Shannon theorem, a central result in quantum information theory that characterizes the resources needed to simulate quantum channels when entanglement is freely available. We derive a universal additive upper bound on the smoothed max-information in terms of the sandwiched Rényi mutual information. This bound yields tighter single-shot results, eliminates the need for the post-selection technique, and leads to a conceptually simpler proof of the quantum reverse Shannon theorem. By consolidating and streamlining earlier approaches, our result provides a clearer and more direct understanding of the resource costs of simulating quantum channels.

Problem

• Simplifying the quantum reverse Shannon theorem proof
• Establishing universal additive bounds for max-information
• Characterizing resource costs for quantum channel simulation

Innovation

• Universal additive bound on smoothed max-information
• Eliminates need for post-selection technique
• Simplifies proof of quantum reverse Shannon theorem