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

Yuhang Yao, Tushita Prasad, Markus Grassl, Syed Jafar, Hua Sun

TL;DR

The space-sharing argument is elaborated upon and a new tight entropic Singleton bound is established for EACC codes with entanglement assistance distributed across a subset of encoders when only local quantum operations are allowed at each encoder.

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.

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

TL;DR

The space-sharing argument is elaborated upon and a new tight entropic Singleton bound is established for EACC codes with entanglement assistance distributed across a subset of encoders when only local quantum operations are allowed at each encoder.

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.
Paper Structure (10 sections, 2 theorems, 13 equations, 2 figures)

This paper contains 10 sections, 2 theorems, 13 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Notations
  4. Entanglement-assisted Classical Communication (EACC)
  5. Saturation of the EACC Singleton Bound
  6. Example
  7. Proof of Theorem \ref{['thm:singleton']}
  8. Asymptotic saturation with large $q$
  9. EACC with Separate Encoders
  10. Discussion

Key Result

Theorem 1

For any admissible $n$, $d$, $c$ with $c\leq n$, $k^* = (1+c/n) (n-d+1)$.

Figures (2)

  • Figure 1: General description of a coding scheme for EACC.
  • Figure 2: EACC coding framework with separate encoders.

Theorems & Definitions (4)

  • Remark 1
  • Theorem 1
  • Theorem 2
  • proof