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Covert Communication Over a Quantum MAC with a Helper

Hassan ZivariFard, Rémi A. Chou, Xiaodong Wang

TL;DR

This work investigates covert classical communication over a quantum multiple-access channel with a helper who can access the private messages of two transmitters. It presents an achievable covert rate region derived from random coding, a quantum packing lemma, and channel resolvability/pinching techniques, demonstrating that positive covert rates are possible on a quantum MAC with a helper. The results unify and extend known classical and quantum MAC covert communication scenarios and reveal that the helper enables covert cooperation that yields nonzero rates under a square-root-like stealth constraint. The methodologies and lemmas developed offer a framework for analyzing covertness in quantum multi-user settings and may influence designs of stealthy quantum communications.

Abstract

We study covert classical communication over a quantum multiple-access channel (MAC) with a helper. Specifically, we consider three transmitters, where one transmitter helps the other two transmitters communicate covertly with a receiver. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish an achievable rate region. Our result recovers as a special case known results for classical communication over classical MACs with a degraded message set, classical communication over quantum MACs, and classical communication over MACs with a helper. To the best of our knowledge, our result is the first to achieve covert communication with positive rates over both classical and quantum MACs.

Covert Communication Over a Quantum MAC with a Helper

TL;DR

This work investigates covert classical communication over a quantum multiple-access channel with a helper who can access the private messages of two transmitters. It presents an achievable covert rate region derived from random coding, a quantum packing lemma, and channel resolvability/pinching techniques, demonstrating that positive covert rates are possible on a quantum MAC with a helper. The results unify and extend known classical and quantum MAC covert communication scenarios and reveal that the helper enables covert cooperation that yields nonzero rates under a square-root-like stealth constraint. The methodologies and lemmas developed offer a framework for analyzing covertness in quantum multi-user settings and may influence designs of stealthy quantum communications.

Abstract

We study covert classical communication over a quantum multiple-access channel (MAC) with a helper. Specifically, we consider three transmitters, where one transmitter helps the other two transmitters communicate covertly with a receiver. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish an achievable rate region. Our result recovers as a special case known results for classical communication over classical MACs with a degraded message set, classical communication over quantum MACs, and classical communication over MACs with a helper. To the best of our knowledge, our result is the first to achieve covert communication with positive rates over both classical and quantum MACs.

Paper Structure

This paper contains 10 sections, 6 theorems, 36 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Main Results
  4. Proof of Theorem \ref{['thm:Achievable']}
  5. Random Codebook Generation
  6. Encoding
  7. Decoding and Error Probability Analysis
  8. Covertness Analysis
  9. Proof of Lemma \ref{['lemma:Packing']}
  10. Proof of Lemma \ref{['lemma:Resolvability']}

Key Result

Theorem 1

Define the rate region $\mathcal{R}_{\textup{q-MAC}}$ as follows, where An inner bound for the covert capacity region of a quantum MAC $\mathcal{N}_{A_{[3]}\to BE}$, depicted in Fig. fig:System_Model, is

Figures (1)

  • Figure 1: Covert communication over a quantum MAC with a helper.

Theorems & Definitions (8)

  • Definition 1
  • Definition 2: Covert Communication
  • Theorem 1
  • Corollary 1: Classical Communication Over a Quantum MAC
  • Corollary 2: Communication Over a classical MAC with a Helper
  • Corollary 3: Covert Communication Over a classical MAC with one message
  • Lemma 1
  • Lemma 2