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A Compact Framework for Analyzing Asynchronous Entanglement Distribution in Quantum Networks

Emma Hughes, William Munizzi, Prineha Narang

TL;DR

This paper tackles the challenge of analyzing asynchronous entanglement distribution in quantum networks under realistic noise. It develops a compact analytical framework that yields a closed-form fidelity expression depending only on the total memory time $T$ and memory dephasing time $T_{dp}$, with an explicit dependence on Bell-state measurement quality through $(\lambda_{BSM})^m$. By comparing sequential and parallel implementations in a linear network, the authors show that parallel distribution consistently achieves higher hashing rates while maintaining similar fidelity, highlighting its practical advantage for near-term quantum networks. The framework accommodates memory dephasing, optical loss, and imperfect BSMs and can be extended to multi-party scenarios and GHZ-type entanglement, offering a scalable tool for routing and protocol design in quantum repeater networks.

Abstract

This work introduces a compact framework for analyzing asynchronous entanglement distribution protocols under realistic error models. We focus on two contemporary protocols: sequential, where entanglement is established one node at a time, and parallel, where all nodes attempt to generate entanglement simultaneously. We derive an analytical expression for the fidelity of distributed entangled states, showing that the fidelity depends only on the total time all qubits spend in memory, rather than the individual memory times for each qubit. This result distills the complex dynamics of entanglement distribution into a compact accessible form, providing an scalable tool for evaluating protocol efficiency. Using this lightweight framework, we analyze the performance of parallel and sequential protocols, demonstrating that parallel distribution consistently outperforms sequential and highlighting the potential of parallel protocols for practical quantum network implementations.

A Compact Framework for Analyzing Asynchronous Entanglement Distribution in Quantum Networks

TL;DR

This paper tackles the challenge of analyzing asynchronous entanglement distribution in quantum networks under realistic noise. It develops a compact analytical framework that yields a closed-form fidelity expression depending only on the total memory time and memory dephasing time , with an explicit dependence on Bell-state measurement quality through . By comparing sequential and parallel implementations in a linear network, the authors show that parallel distribution consistently achieves higher hashing rates while maintaining similar fidelity, highlighting its practical advantage for near-term quantum networks. The framework accommodates memory dephasing, optical loss, and imperfect BSMs and can be extended to multi-party scenarios and GHZ-type entanglement, offering a scalable tool for routing and protocol design in quantum repeater networks.

Abstract

This work introduces a compact framework for analyzing asynchronous entanglement distribution protocols under realistic error models. We focus on two contemporary protocols: sequential, where entanglement is established one node at a time, and parallel, where all nodes attempt to generate entanglement simultaneously. We derive an analytical expression for the fidelity of distributed entangled states, showing that the fidelity depends only on the total time all qubits spend in memory, rather than the individual memory times for each qubit. This result distills the complex dynamics of entanglement distribution into a compact accessible form, providing an scalable tool for evaluating protocol efficiency. Using this lightweight framework, we analyze the performance of parallel and sequential protocols, demonstrating that parallel distribution consistently outperforms sequential and highlighting the potential of parallel protocols for practical quantum network implementations.

Paper Structure

This paper contains 16 sections, 45 equations, 2 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Entanglement Distribution and Noise in Quantum Networks
  3. An Error Model for Entanglement-Based Quantum Networks
  4. A Closed Form Expression for Fidelity in an $n$-Qubit Network
  5. Performance Evaluation Metrics
  6. Efficient Analysis of Asynchronous Entanglement Distribution
  7. Sequential Entanglement Distribution
  8. Parallel Entanglement Distribution
  9. Comparison of Sequential and Parallel Protocols
  10. Impact of Bell State Measurement Imperfections
  11. Discussion
  12. Appendix
  13. Dephasing Error on a Four Qubit Network
  14. Generalization to N-Qubit Networks
  15. Imperfect Bell State Measurement
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Comparisons between asynchronous distribution protocols, conducted using fidelity and hashing rate metrics. Protocols are compared in networks with attenuation length $L_{att} =22$km and internode distance $L=50/N$km, with varying dephasing times $T_{dp}$ and number of nodes $N$. Subfigures (a) and (b) give the fidelity of distributed Bell pairs in the sequential and parallel protocols, respectively. Subfigures (c) and (d) depict corresponding hashing rates. While fidelity is comparable across both protocols, the parallel approach demonstrates a strong advantage in hashing rate.
  • Figure 2: Comparisons of imperfect BSM tolerance in sequential and parallel protocols. Protocols are compared in networks with attenuation length $L_{att} =22$km and internode distance $L=50/N$km, with varying dephasing times $T_{dp}$ and number of nodes $N$. Subfigures (a--c) give the hashing rate for the sequential protocol with increasing $\lambda_{\text{BSM}}$. Subfigures (d--f) show results for the parallel protocol. For sufficiently high $\lambda_{\text{BSM}}$, the parallel protocol is far more robust to imperfect BSM than the sequential.