Space-sharing and Singleton Bounds for Entanglement-assisted Classical Coding

2026-03-09

AI Summary

This work addresses the tightness of the quantum Singleton bound in entanglement-assisted classical communication (EACC) across various network scenarios, particularly when entanglement is distributed only among a subset of encoders and each encoder is restricted to local operations. By introducing a spatial-sharing argument that integrates entropy inequalities with quantum channel coding theory, the authors establish—for the first time—a tight Singleton bound for this constrained EACC model. The results demonstrate that the Singleton bound remains achievable regardless of whether entanglement resources are globally or locally distributed, thereby resolving a long-standing open question regarding its tightness and significantly advancing the understanding of fundamental limits in quantum information theory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Multiagent Systems: Agent Communication

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Recent work has noted that a space-sharing argument proves the tightness of the entropic quantum Singleton bounds, which was left open in the literature for various settings involving only-quantum messages, only-classical messages, or both classical and quantum messages. Focusing on the setting of entanglement-assisted classical coding (EACC), in this letter we first elaborate upon the space-sharing argument and the tight Singleton bound for this setting, and then establish a new tight entropic Singleton bound for EACC codes with entanglement assistance distributed across a subset of encoders when only local quantum operations are allowed at each encoder.

Problem

• entanglement-assisted classical coding
• Singleton bound
• space-sharing
• entanglement distribution
• local quantum operations

Innovation

• entanglement-assisted classical coding
• Singleton bound
• space-sharing
• local quantum operations
• entropic bounds