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Experimental composable key distribution using discrete-modulated continuous variable quantum cryptography

Adnan A. E. Hajomer, Florian Kanitschar, Nitin Jain, Michael Hentschel, Runjia Zhang, Norbert Lütkenhaus, Ulrik L. Andersen, Christoph Pacher, Tobias Gehring

TL;DR

This work demonstrates the first experimental implementation of a four‑state discrete‑modulated CVQKD system with composable finite‑size security against collective attacks over a $20\,\text{km}$ fiber, achieving $N \approx 2.3 \times 10^{9}$ states and a positive key rate of $\$11.04\times 10^{-3}$ bits/symbol, producing about $0.94\,\text{Mbit}$ of composable secure key. It integrates an end‑to‑end protocol stack—state preparation, energy/acceptance tests, postselection, LDPC‑based reconciliation, and universal hashing—within a DSP‑driven, telecom‑friendly hardware platform operating at $125\,\text{MBaud}$ with a $1\,\text{GS/s}$ DAC/ADC, and a $20\,\text{km}$ fiber channel. The security argument relies on a composable finite‑size proof against i.i.d. collective attacks, leveraging an SDP bound over the acceptance set and a careful allocation of the total security parameter $\epsilon=10^{-10}$ among sub‑protocols. The results advance practical DM CVQKD toward large‑scale, high‑rate, quantum‑safe networks compatible with standard telecom components, and highlight avenues for improvement such as higher constellation sizes and multi‑user architectures.

Abstract

Establishing secure data communication necessitates secure key exchange over a public channel. Quantum key distribution (QKD), which leverages the principles of quantum physics, can achieve this with information-theoretic security. The discrete modulated (DM) continuous variable (CV) QKD protocol, in particular, is a suitable candidate for large-scale deployment of quantum-safe communication due to its simplicity and compatibility with standard high-speed telecommunication technology. Here, we present the first experimental demonstration of a four-state DM CVQKD system, successfully generating composable finite-size keys, secure against collective attacks over a 20 km fiber channel with 2.3 \times 10^{9} coherent quantum states, achieving a positive composable key rate of 11.04 \times 10^{-3} bits/symbol. This accomplishment is enabled by using an advanced security proof, meticulously selecting its parameters, and the fast, stable operation of the system. Our results mark a significant step toward the large-scale deployment of practical, high-performance, cost-effective, and highly secure quantum key distribution networks using standard telecommunication components.

Experimental composable key distribution using discrete-modulated continuous variable quantum cryptography

TL;DR

This work demonstrates the first experimental implementation of a four‑state discrete‑modulated CVQKD system with composable finite‑size security against collective attacks over a fiber, achieving states and a positive key rate of 11.04\times 10^{-3}0.94\,\text{Mbit}125\,\text{MBaud}1\,\text{GS/s}20\,\text{km}\epsilon=10^{-10}$ among sub‑protocols. The results advance practical DM CVQKD toward large‑scale, high‑rate, quantum‑safe networks compatible with standard telecom components, and highlight avenues for improvement such as higher constellation sizes and multi‑user architectures.

Abstract

Establishing secure data communication necessitates secure key exchange over a public channel. Quantum key distribution (QKD), which leverages the principles of quantum physics, can achieve this with information-theoretic security. The discrete modulated (DM) continuous variable (CV) QKD protocol, in particular, is a suitable candidate for large-scale deployment of quantum-safe communication due to its simplicity and compatibility with standard high-speed telecommunication technology. Here, we present the first experimental demonstration of a four-state DM CVQKD system, successfully generating composable finite-size keys, secure against collective attacks over a 20 km fiber channel with 2.3 \times 10^{9} coherent quantum states, achieving a positive composable key rate of 11.04 \times 10^{-3} bits/symbol. This accomplishment is enabled by using an advanced security proof, meticulously selecting its parameters, and the fast, stable operation of the system. Our results mark a significant step toward the large-scale deployment of practical, high-performance, cost-effective, and highly secure quantum key distribution networks using standard telecommunication components.

Paper Structure

This paper contains 20 sections, 3 theorems, 20 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. DM CVQKD Protocols and Composable Secure Key
  3. Protocol Description
  4. Security Argument
  5. CVQKD System implementation
  6. Sender
  7. Receiver
  8. System calibration and measurements
  9. Post-Processing
  10. Energy Test and Acceptance Test
  11. Key Mapping & Post Selection
  12. Reverse Reconciliation
  13. Error Verification (Confirmation) with Polynomial Hashing
  14. Privacy Amplification
  15. Results
  16. ...and 5 more sections

Key Result

Theorem 1

Let $\mathcal{H}_A$ and $\mathcal{H}_B$ be separable Hilbert spaces and let $\epsilon_{\mathrm{ET}}, \epsilon_{\mathrm{AT}}, \bar{\epsilon}, \epsilon_{\mathrm{EC}}, \epsilon_{\mathrm{PA}} > 0$. The objective QKD protocol is $\epsilon_{\mathrm{EC}} + \max\left\{\frac{1}{2}\epsilon_{\mathrm{PA}}+\bar{ where $\delta^{\mathrm{EC}}_{\mathrm{leak}}$ takes the classical error correction cost into account

Figures (3)

  • Figure 1: Discrete modulated continuous variable quantum key distribution protocol with composable security. See the main text for the details.
  • Figure 2: DM CVQKD set-up. Schematic of the quantum key distribution (QKD) system, detailing all key components and digital signal processing (DSP) modules. At Alice's side: CW laser (continuous wave laser), IQ modulator (in-phase and quadrature modulator), VOA (variable optical attenuator), Faraday isolator (indicated by the arrow), DAC (digital-to-analog converter) and ABC (automatic bias controller). At Bob's side: CW laser used as a local oscillator (LO), BD (balanced detector), polarization controller (PC), and ADC (analog-to-digital converter). Alice's and Bob's stations utilize polarization-maintaining fiber (PMF) components, while the quantum channel is a spool of standard single-mode fiber (SMF). All electronic connections (EC) are represented by black lines.
  • Figure 3: Secure Key Fraction (SKF $=\ell / N$) vs. radial postselection parameter for different testing ratios $r_T$. The green curves represent the theoretical SKF for assumed (constant) $92\%$ error-correction efficiency, the orange dots illustrate the secure key fraction for the experimental data. The numbers in the balloons state the average efficiency $\bar{\beta}$ of LDPC codes used for error-correction, while the color of the balloons indicates the code rate $R$.

Theorems & Definitions (3)

  • Theorem 1: Security against i.i.d. collective attacks Kanitschar2023
  • Theorem 2: Noise robust Energy Test Kanitschar2023
  • Theorem 3: Acceptance Test Kanitschar2023