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Achievable Identification Rates in Noisy Bosonic Broadcast Channels

Zuhra Amiri, Janis Nötzel

TL;DR

This work studies identification capacity for a noisy bosonic broadcast channel with a power constraint $E$ and coherent-state inputs. It develops a discretization-based approach, augmented by an energy-threshold mechanism and quantum hypothesis testing, to derive an achievable identification region whose rates are bounded by Holevo informations on the marginal channels, and shows convergence to continuous Gaussian-ensemble bounds $R_i \le g(\tau_i E + N_i) - g(N_i)$ as the discretization becomes dense. The results extend finite-dimensional identification theory to infinite-dimensional bosonic systems and provide a framework for analyzing ID in practical quantum optical networks. Practically, the approach enables reliable message presence verification in quantum networks while accounting for energy constraints and channel noise, with future work pointing to alternative encodings and experimental validation.

Abstract

Identification in quantum communication enables receivers to verify the presence of a message without decoding its entire content. While identification capacity has been explored for classical and finite-dimensional quantum channels, its behaviour in bosonic systems remains less understood. This work analyses identification over noisy bosonic broadcast channels using coherent states. We derive achievable identification rate regions while ensuring error probabilities remain bounded, even in an infinite-dimensional setting. Our approach leverages quantum hypothesis testing and approximates the infinite sender alphabet with discrete subsets to maintain power constraints.

Achievable Identification Rates in Noisy Bosonic Broadcast Channels

TL;DR

This work studies identification capacity for a noisy bosonic broadcast channel with a power constraint and coherent-state inputs. It develops a discretization-based approach, augmented by an energy-threshold mechanism and quantum hypothesis testing, to derive an achievable identification region whose rates are bounded by Holevo informations on the marginal channels, and shows convergence to continuous Gaussian-ensemble bounds as the discretization becomes dense. The results extend finite-dimensional identification theory to infinite-dimensional bosonic systems and provide a framework for analyzing ID in practical quantum optical networks. Practically, the approach enables reliable message presence verification in quantum networks while accounting for energy constraints and channel noise, with future work pointing to alternative encodings and experimental validation.

Abstract

Identification in quantum communication enables receivers to verify the presence of a message without decoding its entire content. While identification capacity has been explored for classical and finite-dimensional quantum channels, its behaviour in bosonic systems remains less understood. This work analyses identification over noisy bosonic broadcast channels using coherent states. We derive achievable identification rate regions while ensuring error probabilities remain bounded, even in an infinite-dimensional setting. Our approach leverages quantum hypothesis testing and approximates the infinite sender alphabet with discrete subsets to maintain power constraints.

Paper Structure

This paper contains 7 sections, 6 theorems, 33 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notation and Channel Model
  3. Definitions and Lemmas
  4. Results
  5. Proofs
  6. Discussion
  7. Conclusion and Future Work

Key Result

Lemma 1

Let $\rho$ be a density operator and $0 \leq \Pi \leq \mathbf{1}$ be a measurement operator. If ${\mathrm{tr}}(\Pi \rho) \geq 1 - \epsilon$ for some $\epsilon \geq 0$, then where $\| \cdot \|_1$ denotes the trace norm.

Figures (1)

  • Figure 1: A plot of the achievable identification rate regions for a noisy bosonic broadcast channel with additive noise $N_1 = N_2 = 0.1$, for average input photon numbers $E = 0.5$ (green region) and $E = 0.25$ (red region), as shown in Theorem \ref{['thm:main']}.

Theorems & Definitions (9)

  • Lemma 1: Gentle Operator Lemma watts2024quantum
  • Lemma 2: see bracher2017
  • Definition 3: Capacity of Noisy Bosonic Channel Giovannetti_2014
  • Theorem 4
  • Theorem 5
  • Lemma 6
  • Lemma 7: See nötzel2025infinitefoldquantumadvantageclassical
  • proof : Proof of Theorem \ref{['thm:approximate-main']}
  • proof : Proof of Theorem \ref{['thm:main']}