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Simulation of Quantum Repeater Networks under Decoherence and Purification Constraints

Wenhan Li, Shiyu Zhang

TL;DR

The paper addresses the challenge of distributing high-fidelity entanglement over long distances using quantum repeaters under realistic decoherence and purification constraints. It introduces a configurable simulation framework that models BK entanglement generation, entanglement swapping, continuous-time depolarization, and BBPSSW purification across repeater chains, enabling quantitative trade-offs between fidelity, time, and resource use. Key findings show that memory decoherence strongly constrains performance, purification costs grow rapidly with distance and swap depth, and a practical noise-tolerance boundary exists around $T_{\text{depol}} \ge 4$ ms for achieving $F_{\text{end}} \ge 0.9$. The work provides a flexible tool for evaluating repeater designs and highlights the need for more advanced approaches such as quantum error correction or all-photonic/hybrid architectures for scalability.

Abstract

Long-distance quantum communication requires reliable entanglement distribution, but direct generation with protocols such as Barrett--Kok suffers from exponentially decreasing success probability with distance, making it impractical over hundreds of kilometers. Quantum repeaters address this by segmenting the channel and combining entanglement generation, swapping, and purification. In this work, we present a simulation framework for chain-based repeaters under continuous-time depolarizing noise. Our model implements heralded entanglement generation, Bell-state swapping, and multi-round purification, with configurable chain length, noise levels, and purification depth. Numerical results highlight how memory decoherence constrains performance, how purification mitigates fidelity loss, and how time and entanglement costs scale with distance. While simplified, the framework offers a flexible tool for exploring trade-offs in repeater design and provides a basis for extensions toward more complex network scenarios.

Simulation of Quantum Repeater Networks under Decoherence and Purification Constraints

TL;DR

The paper addresses the challenge of distributing high-fidelity entanglement over long distances using quantum repeaters under realistic decoherence and purification constraints. It introduces a configurable simulation framework that models BK entanglement generation, entanglement swapping, continuous-time depolarization, and BBPSSW purification across repeater chains, enabling quantitative trade-offs between fidelity, time, and resource use. Key findings show that memory decoherence strongly constrains performance, purification costs grow rapidly with distance and swap depth, and a practical noise-tolerance boundary exists around ms for achieving . The work provides a flexible tool for evaluating repeater designs and highlights the need for more advanced approaches such as quantum error correction or all-photonic/hybrid architectures for scalability.

Abstract

Long-distance quantum communication requires reliable entanglement distribution, but direct generation with protocols such as Barrett--Kok suffers from exponentially decreasing success probability with distance, making it impractical over hundreds of kilometers. Quantum repeaters address this by segmenting the channel and combining entanglement generation, swapping, and purification. In this work, we present a simulation framework for chain-based repeaters under continuous-time depolarizing noise. Our model implements heralded entanglement generation, Bell-state swapping, and multi-round purification, with configurable chain length, noise levels, and purification depth. Numerical results highlight how memory decoherence constrains performance, how purification mitigates fidelity loss, and how time and entanglement costs scale with distance. While simplified, the framework offers a flexible tool for exploring trade-offs in repeater design and provides a basis for extensions toward more complex network scenarios.

Paper Structure

This paper contains 16 sections, 15 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Modeling Assumptions and Implementation
  3. Atomic Entanglement Generation
  4. Network Simulation
  5. Continuous-Time Depolarization Noise
  6. Purification Protocol
  7. Purification Rounds: Ideal vs. Actual Execution under Decoherence
  8. Evaluation Metrics
  9. Implementation and Code Availability
  10. Experiments and Results
  11. Effect of $T_{depol}$ on Performance
  12. Noise Tolerance Boundary
  13. Minimum Werner-Pair Cost and Time Efficiency
  14. Influence of Distance on Entanglement Generation
  15. Effect of the Number of Quantum Repeaters
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Impact of varying $T_{depol}$ on generation time, fidelity, and purification cost.
  • Figure 2: Effect of total distance $L$ on entanglement generation performance.