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The Interference Channel with Entangled Transmitters

Jonas Hawellek, Athin Mohan, Hadi Aghaee, Christian Deppe

TL;DR

This work studies a classical interference channel with two transmitters and two receivers that share entanglement, formulating an entanglement-assisted capacity region $\mathcal{C}_{ET}$. It extends the Han-Kobayashi framework to the entangled setting, deriving an inner bound $\mathcal{R}_{\text{ET-HK}}$ via rate-splitting, superposition coding, and entanglement-assisted encoding POVMs, and an outer bound $\mathcal{R}_{\text{ET-o}}$ that constrains the region under shared entanglement. A key result is that the union over pure states suffices for the achievable region, with a finite-time-sharing bound $|\mathcal{V}_0|\le 7$; the framework is illustrated by a magic-square-game-based channel showing a quantum advantage: the classical sum-rate bound is $R_1+R_2\le 3.02$, while entanglement enables $R_1+R_2=2\log_2 3\approx3.17$. The findings indicate that quantum resources can strictly enlarge capacity regions in networked communication and motivate further exploration of finite-alphabet bounds and robustness to entanglement noise in realistic systems.

Abstract

This paper explores communication over a two-sender, two-receiver classical interference channel, enhanced by the availability of entanglement resources between transmitters. The central contributions are an inner and outer bound on the capacity region for a general interference channel with entangled transmitters. It addresses the persistent challenge of the lack of a general capacity formula, even in the purely classical case, and highlights the striking similarities in achievable rate expressions when assessing quantum advantages. Through a concrete example, it is shown that entanglement can significantly boost performance in certain types of channels.

The Interference Channel with Entangled Transmitters

TL;DR

This work studies a classical interference channel with two transmitters and two receivers that share entanglement, formulating an entanglement-assisted capacity region . It extends the Han-Kobayashi framework to the entangled setting, deriving an inner bound via rate-splitting, superposition coding, and entanglement-assisted encoding POVMs, and an outer bound that constrains the region under shared entanglement. A key result is that the union over pure states suffices for the achievable region, with a finite-time-sharing bound ; the framework is illustrated by a magic-square-game-based channel showing a quantum advantage: the classical sum-rate bound is , while entanglement enables . The findings indicate that quantum resources can strictly enlarge capacity regions in networked communication and motivate further exploration of finite-alphabet bounds and robustness to entanglement noise in realistic systems.

Abstract

This paper explores communication over a two-sender, two-receiver classical interference channel, enhanced by the availability of entanglement resources between transmitters. The central contributions are an inner and outer bound on the capacity region for a general interference channel with entangled transmitters. It addresses the persistent challenge of the lack of a general capacity formula, even in the purely classical case, and highlights the striking similarities in achievable rate expressions when assessing quantum advantages. Through a concrete example, it is shown that entanglement can significantly boost performance in certain types of channels.

Paper Structure

This paper contains 21 sections, 8 theorems, 46 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Definitions
  3. Basic Definitions
  4. Interference Channel with Entangled Transmitters
  5. Bounds on the Capacity of the Classical Interference Channel
  6. Han-Kobayashi Inner Bound
  7. Outer Bound
  8. Main Results
  9. Inner Bound
  10. Outer Bound
  11. Channel Example
  12. Magic Square Game
  13. Channel Model and Capacity Results
  14. Proof of Theorem \ref{['thm:InnerBound']} (Inner Bound)
  15. Code Construction
  16. ...and 6 more sections

Key Result

Lemma 1

Any rate pair $(R_1,R_2) \in \mathcal{R}_{\text{HK}}$ is achievable for the discrete memoryless IC $P_{Y_1,Y_2|X_1,X_2}$ElGamal_Kim_2011. Hence, the capacity region $\mathcal{C}$ of the general discrete memoryless IC satisfies

Figures (2)

  • Figure 1: The classical interference channel $P_{Y_1,Y_2|X_1,X_2}$ with entanglement resources (quantum systems) shared between the transmitters. The entanglement resources of transmitter 1 and transmitter 2 are marked in red and blue, respectively.
  • Figure 2: Superposition coding at transmitter 1. Message $m_1'$ is intended to be decoded by both receivers and is encoded into distant cloud center codewords $u_1^n$. Message $m_1"$ is decoded solely by receiver 1 after the corresponding cloud center ($m_1'$) has already been determined.

Theorems & Definitions (13)

  • Definition 1
  • Lemma 1
  • Remark 1
  • Lemma 2
  • Theorem 3
  • Lemma 4
  • Lemma 5
  • Remark 2
  • Remark 3
  • Theorem 6
  • ...and 3 more