Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Entanglement-Assisted Bosonic MAC: Achievable Rates and Covert Communication

Yu-Chen Shen, Matthieu R. Bloch

TL;DR

This work analyzes covert communication over a two-user entanglement-assisted bosonic MAC, establishing a closed-form, single-letter rate region for high-order PSK modulation and showing that in the low-photon regime the region becomes a rectangle matching point-to-point EA covert capacities. It extends to a two-layer covert coding framework that achieves an aggregate $O(\sqrt{n}\log n)$ covert throughput while revealing a linear trade-off in energy allocation between the two senders. The approach combines Gaussian quantum information tools, one-shot resolvability and reliability bounds, and a careful truncation to finite dimensions, enabling explicit second-order and scaling results. The findings advance understanding of multi-user covert quantum communications and quantify how entanglement assistance and joint covertness constraints shape achievable rates and resource sharing in practical scenarios.

Abstract

We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of \(O(\sqrt{n} \log n)\) covert bits with the block length $n$ for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.

Entanglement-Assisted Bosonic MAC: Achievable Rates and Covert Communication

TL;DR

This work analyzes covert communication over a two-user entanglement-assisted bosonic MAC, establishing a closed-form, single-letter rate region for high-order PSK modulation and showing that in the low-photon regime the region becomes a rectangle matching point-to-point EA covert capacities. It extends to a two-layer covert coding framework that achieves an aggregate covert throughput while revealing a linear trade-off in energy allocation between the two senders. The approach combines Gaussian quantum information tools, one-shot resolvability and reliability bounds, and a careful truncation to finite dimensions, enabling explicit second-order and scaling results. The findings advance understanding of multi-user covert quantum communications and quantify how entanglement assistance and joint covertness constraints shape achievable rates and resource sharing in practical scenarios.

Abstract

We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of \(O(\sqrt{n} \log n)\) covert bits with the block length for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.
Paper Structure (15 sections, 13 theorems, 104 equations, 1 table)

This paper contains 15 sections, 13 theorems, 104 equations, 1 table.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. High-rate PSK over bosonic MAC
  4. Covert Communication over bosonic MAC
  5. Proof of Theorem \ref{['thm:main']}
  6. Code Construction
  7. Lemmas
  8. Bob's Projection Channel
  9. Reliability for Layer 1
  10. Covertness Analysis
  11. Reliability for Layer 2 and Total Error Analysis
  12. Throughput Analysis
  13. Layer 1
  14. Layer 2
  15. Existence Argument

Key Result

Lemma 2.1

Cheng2023QuantumGeorge2024CoherentSen2018Unions Fix $\varepsilon \in (0,1), \eta\in(0,\varepsilon), \delta \in (0,1)$, and $\delta' \in (0,\delta)$. Suppose a c-q state $\rho_{XYA_XA_Y}$ and a channel $\mathcal{G}: \rho_{XYA_XA_Y} \mapsto \rho_{XYZW}$, where $A_X$ and $A_Y$ are mutually independent and Here, $\hat{\rho}_W$ denotes the induced soft-covering state on the system $W$, defined as the

Theorems & Definitions (27)

  • Lemma 2.1
  • proof : Proof of Lemma \ref{['lemm:reliable_resolvable']}
  • Definition 3.1: EA-MAC Code, Reliability, and Rates
  • Remark 3.2: Variance Penalty of Heterodyne Detection
  • Lemma 3.3: Achievable Sum-Rate Lower Bound
  • Proposition 3.4: Proposition $1$ of Su2024Achievable
  • Proposition 3.5: Proposition $2$ of Su2024Achievable
  • Theorem 3.6: EA-MAC Achievable Rate Region
  • Lemma 3.7: Asymptotic Scaling of Mutual Information
  • proof
  • ...and 17 more