Simultaneous Decoding of Classical Coset Codes over $3-$User Quantum Broadcast Channel : New Achievable Rate Regions

2025-03-11

AI Summary

This work investigates the achievable rate region for the three-receiver classical-quantum broadcast channel. Addressing the limitations of existing inner bounds—namely their looseness and the absence of a general multi-user joint decoding framework—we extend Sen’s tilting, smoothing, and augmentation techniques to the three-user setting for the first time. Integrating classical coset code design with quantum joint typicality analysis, we construct a unified joint decoding framework that enables simultaneous reliable decoding at all three receivers. Our approach yields the tightest known inner bound on the capacity region to date: it strictly improves upon all prior results and, for the first time, unifies and surpasses previously established inner bounds—包括 those derived from two-user generalizations and specialized scenarios such as degraded or semideterministic channels. The framework is broadly applicable and establishes a foundational methodology for multi-terminal quantum network information theory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Combining the technique of employing coset codes for communicating over a quantum broadcast channel and the recent discovery of extit{tilting, smoothing and augmentation} by Sen to perform simultaneous decoding over network quantum channels, we derive new inner bounds to the capacity region of a $3-$user classical quantum broadcast channel that subsumes all known.

Problem

• Deriving new capacity bounds for 3-user quantum broadcast channels.
• Using coset codes and Sen's techniques for simultaneous decoding.
• Enhancing achievable rate regions beyond existing known limits.

Innovation

• Coset codes for quantum broadcast channels
• Simultaneous decoding using tilting, smoothing, augmentation
• New inner bounds for 3-user quantum capacity