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Composable Continuous-Variable Multi-User QKD with Discrete Modulation: Theory and Implementation

Florian Kanitschar, Adnan A. E. Hajomer, Michael Hentschel, Tobias Gehring, Christoph Pacher

TL;DR

The paper addresses scalable, secure quantum networks by extending discrete-modulated continuous-variable QKD to multi-user (point-to-multipoint) settings. It presents four trust scenarios, develops both lossless and noisy channel security analyses, and employs a SDP-based, dimension-reduction approach to establish composable finite-size security bounds. An experimental validation over a passive optical network with two receivers achieves $2.185\times10^{-3}$ bits per symbol ($0.273$ Mbit/s) with total security parameter $\epsilon=10^{-10}$, evidencing practicality with off-the-shelf telecom components. The work demonstrates that DM-CVQKD can support multiple users in urban-scale networks, paving the way for scalable, secure quantum networking using discrete modulation and standard hardware.

Abstract

Establishing scalable, secure quantum networks requires advancing beyond conventional point-to-point quantum key distribution (QKD) protocols toward point-to-multipoint QKD protocols. Here, we generalize a well-established discrete-modulated continuous-variable (CV) QKD protocol from the point-to-point to the point-to-multipoint setting. We present a comprehensive security analysis across four trust scenarios and derive secret key rates for both loss-only and noisy channels, in the asymptotic and composable finite-size regimes. Experimentally, we validate the protocol in a passive optical network with 10 km access links, achieving a composable secure key rate of $2.185 \times 10^{-3}$ bits per symbol (0.273 Mbit/s) against independent and identically distributed collective attacks. Our results demonstrate that discrete-modulated CV-QKD can support access networks with multiple users while relying solely on cost-efficient, off-the-shelf telecommunication components, paving the way toward practical, scalable, and secure quantum networks.

Composable Continuous-Variable Multi-User QKD with Discrete Modulation: Theory and Implementation

TL;DR

The paper addresses scalable, secure quantum networks by extending discrete-modulated continuous-variable QKD to multi-user (point-to-multipoint) settings. It presents four trust scenarios, develops both lossless and noisy channel security analyses, and employs a SDP-based, dimension-reduction approach to establish composable finite-size security bounds. An experimental validation over a passive optical network with two receivers achieves bits per symbol ( Mbit/s) with total security parameter , evidencing practicality with off-the-shelf telecom components. The work demonstrates that DM-CVQKD can support multiple users in urban-scale networks, paving the way for scalable, secure quantum networking using discrete modulation and standard hardware.

Abstract

Establishing scalable, secure quantum networks requires advancing beyond conventional point-to-point quantum key distribution (QKD) protocols toward point-to-multipoint QKD protocols. Here, we generalize a well-established discrete-modulated continuous-variable (CV) QKD protocol from the point-to-point to the point-to-multipoint setting. We present a comprehensive security analysis across four trust scenarios and derive secret key rates for both loss-only and noisy channels, in the asymptotic and composable finite-size regimes. Experimentally, we validate the protocol in a passive optical network with 10 km access links, achieving a composable secure key rate of bits per symbol (0.273 Mbit/s) against independent and identically distributed collective attacks. Our results demonstrate that discrete-modulated CV-QKD can support access networks with multiple users while relying solely on cost-efficient, off-the-shelf telecommunication components, paving the way toward practical, scalable, and secure quantum networks.
Paper Structure (28 sections, 1 theorem, 60 equations, 12 figures, 2 tables)

This paper contains 28 sections, 1 theorem, 60 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Lossy, noise-free channel
  4. Lossy and noisy channel
  5. Network implementation
  6. Transmitter
  7. Receivers
  8. Post-Processing
  9. Message Authentication
  10. Energy Test and Acceptance Test
  11. Postselection & Key Mapping
  12. Error Correction & Confirmation
  13. Privacy Amplification
  14. Results
  15. Discussion
  16. ...and 13 more sections

Key Result

Lemma 1

For $\ket{b_{z}}_E$ as defined above and $z_1,z_2 \in \left[N_{\mathrm{St}}\right]_{-1}$ we have $z_1 \neq z_2 ~\Rightarrow ~ \ket{b_{z_1}}_E \perp \ket{b_{z_2}}_E$.

Figures (12)

  • Figure 1: (a) Illustration of different trust scenarios, with a) and c) as special cases of b) for $M_B = 1$ and $M_B = N_B$. (b) Protocol description.
  • Figure 2: Schematic of the experimental setup for multi-user DM-CVQKD. Refer to the main text for a detailed description.
  • Figure 3: QPSK key rate for a single Bob vs transmission distance for the loss-only channel.
  • Figure 4: Achievable secure key rate vs. total number of Bobs in three different scenarios: loss-only asymptotic, loss and noise asymptotic, loss and noise finite-size, while two Bobs trust each other. The distance between the central node and each Bob was fixed to $10$km and the curves were optimized over the coherent state amplitude $|\alpha|$.
  • Figure 5: Achievable secure key rate vs. transmission distance in the asymptotic (solid curves) and the finite-size regime (dashed curves). Each data point was optimized over the coherent state amplitude $|\alpha|$ as well as over the postselection parameter $\Delta_r$.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Lemma 1
  • proof