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Fidelity-Age-Aware Scheduling in Quantum Repeater Networks

Ozgur Ercetin, Zafer Gedik

TL;DR

The Fidelity-Age metric, which measures this interval for states whose fidelity exceeds a threshold Fmin, is introduced, which provides a tractable, physically grounded metric for reliable and timely entanglement delivery in quantum networks.

Abstract

Quantum repeater networks distribute entanglement over long distances but must balance fidelity, delay, and resource contention. Prior work optimized throughput and end-to-end fidelity, yet little attention has been paid to the freshness of entanglement-the time since a usable Bell pair was last delivered. We introduce the Fidelity-Age (FA) metric, which measures this interval for states whose fidelity exceeds a threshold Fmin. A renewal formulation links slot-level success probability to long-run average FA, enabling a stochastic control problem that minimizes FA under budget and memory limits. Two lightweight schedulers, FA-THR and FA-INDEX, approximate Lyapunov-drift-optimal control. Simulations on slotted repeater grids show that FA-aware scheduling preserves throughput while reducing extreme-age events by up to two orders of magnitude. Fidelity-Age thus provides a tractable, physically grounded metric for reliable and timely entanglement delivery in quantum networks.

Fidelity-Age-Aware Scheduling in Quantum Repeater Networks

TL;DR

The Fidelity-Age metric, which measures this interval for states whose fidelity exceeds a threshold Fmin, is introduced, which provides a tractable, physically grounded metric for reliable and timely entanglement delivery in quantum networks.

Abstract

Quantum repeater networks distribute entanglement over long distances but must balance fidelity, delay, and resource contention. Prior work optimized throughput and end-to-end fidelity, yet little attention has been paid to the freshness of entanglement-the time since a usable Bell pair was last delivered. We introduce the Fidelity-Age (FA) metric, which measures this interval for states whose fidelity exceeds a threshold Fmin. A renewal formulation links slot-level success probability to long-run average FA, enabling a stochastic control problem that minimizes FA under budget and memory limits. Two lightweight schedulers, FA-THR and FA-INDEX, approximate Lyapunov-drift-optimal control. Simulations on slotted repeater grids show that FA-aware scheduling preserves throughput while reducing extreme-age events by up to two orders of magnitude. Fidelity-Age thus provides a tractable, physically grounded metric for reliable and timely entanglement delivery in quantum networks.
Paper Structure (35 sections, 1 theorem, 38 equations, 6 figures, 1 table)

This paper contains 35 sections, 1 theorem, 38 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Qubits, Bell States, and Fidelity
  4. Freshness and the Fidelity-Age Metric
  5. Related Work
  6. System Model
  7. Network Architecture
  8. Probabilistic Slotted Graph Model
  9. Internal phase: purification and swapping
  10. Usable deliveries and success events
  11. Controller Actions and Constraints
  12. Homogeneous and heterogeneous regimes
  13. Problem Statement
  14. Usable-delivery process
  15. Fidelity-Age (FA)
  16. ...and 20 more sections

Key Result

Theorem 1

Fix a slot duration $\Delta>0$ and a stationary policy $\phi$. Let $Y_t\in\{0,1\}$ be the usable-delivery indicator from Sec. sec:usable and let $\tau=\inf\{\ell\ge 1:\,Y_{t+\ell}=1\mid Y_t=1\}$ be the inter-delivery time (in slots). Assume the underlying state process is stationary and ergodic under $\phi$, that $0<\Pr\{Y_t=1\}<1$, and that $\mathbb{E}[\tau]<\infty$ and $\mathbb{E}[\tau^2]<\inft

Figures (6)

  • Figure 1: $3{\times}3$ grid topology, $|P|{=}16$ source–destination pairs, attempt budget $R{=}8$ per slot ($R/|P|{=}0.5$), $q{=}0.95$, $F_{\min}{=}0.75$, no purification. Comparison of flow-age distributions and throughput–tail-age frontiers across scheduling policies.
  • Figure 2: $3{\times}3$ grid topology with $|P|{=}16$ flows and attempt-budget ratios $R/|P|{\in}\{0.5,1.0\}$; $q{=}0.95$, $F_{\min}{=}0.75$, no purification. Comparison of fairness and starvation behavior across scheduling policies under varying network load.
  • Figure 3: $3{\times}3$ grid, $|P|{=}8$, attempt-budget ratio $R/|P|{=}1$, BSM success $q{=}0.95$, purification success $p_{\mathrm{pur}}{=}0.8$, and fidelity increment $\Delta F{=}0.08$. Comparison of latency and throughput effects as the fidelity threshold $F_{\min}$ varies under FA-INDEX control.
  • Figure 4: $3{\times}3$ grid topology with random link lengths $L(e){\in}[10,80]$ km, producing path lengths $k{\in}\{2,3,4,6\}$; $|P|{=}8$, $R/|P|{=}0.5$, BSM success $q{=}0.9$, no purification. Comparison of latency and fairness across policies under heterogeneous end-to-end distances.
  • Figure 5: $3{\times}3$ grid topology, $|P|{=}8$, attempt-budget ratio $R/|P|{=}1$, BSM success $q{=}0.9$, no purification, memory delay $T{\in}\{2,4,8\}$ slots, and coherence times $T_{2}{\in}\{50,100,200\}$ ms. Comparison of latency and throughput degradation under finite-memory effects for FA-INDEX and other schedulers.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Remark 1: Independence
  • Remark 2: Stationarity
  • Theorem 1: FA renewal identity
  • proof : Proof sketch