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

TL;DR

This paper investigates the limits of entanglement-assisted classical coding, establishing new tight bounds on code performance using space-sharing arguments, especially when entanglement is distributed across multiple encoders with local quantum operations.

Contribution

It extends the space-sharing argument to derive a new tight entropic Singleton bound for entanglement-assisted classical codes with distributed entanglement and local operations.

Findings

Proved the tightness of the entropic quantum Singleton bounds.

Established a new tight Singleton bound for EACC with distributed entanglement.

Clarified the role of local quantum operations in code performance.

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.