Adaptive Resource and Memory Control for Stability in Quantum Entanglement Distribution

Abstract

We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing memory decoherence, while entanglement requests arrive according to Poisson and bursty ON--OFF processes. Using a queueing-theoretic framework, we couple physical-layer memory dynamics with congestion-dependent service behavior to analyze stability, delay, and fidelity trade-offs. Operating regimes are characterized in terms of the load parameter, showing that fixed cutoff policies impose a fundamental fidelity--latency trade-off together with strict stability limits. Queue-aware adaptive control strategies are then introduced that dynamically adjust memory cutoff times and the number of parallel entanglement-generation channels. Cutoff adaptation restores stability near critical load by trading fidelity for service capacity, whereas resource scaling increases capacity without degrading entanglement quality. Under bursty traffic, joint adaptation suppresses delay spikes while activating additional channels only during congestion periods. The framework is further extended to a two-user shared-resource scenario in which independent traffic flows compete for a common resource pool. Stability is determined by aggregate load, while adaptive resource redistribution stabilizes queues that diverge under fixed partitioning. These results provide a queue-aware congestion-control perspective for adaptive resource management in quantum networks.

Figures (7)

• Figure 1: Minimal quantum repeater connecting Alice and Charlie to Bob separated by a distance $2L$.
• Figure 2: Steady-state fidelity versus average latency for a fixed number of channels $N=5$, obtained by varying the memory cutoff time $\tau$.
• Figure 3: Monte Carlo mean queue length $\mathbb{E}[Q(t)]$ under the fixed policy for three arrival rates $\lambda\text{ with}N_{\text{fix}}=16$ and $\tau=0.5T_{2}$. For subcritical load ($\lambda=4.5\times10^{4}$), the queue remains bounded and stabilizes. Near the critical regime ($\lambda=9.1\times10^{4}$), the queue exhibits slow growth, indicating marginal stability. In the supercritical regime ($\lambda=10^{5}$), the mean queue grows approximately linearly in time, signaling instability due to arrival rate exceeding service capacity.
• Figure 4: Comparison between a fixed-cutoff baseline and a queue-aware adaptive policy across different traffic regimes. Panels (a)--(c) report the temporal evolution of fidelity (left) and delay (right) for the two policies.(a) Critical regime with a fixed number of parallel attempts $N$. Inset (left): time evolution of the adaptive cutoff $\tau(t)$. (b) Supercritical regime with a fixed number of parallel attempts $N$. Inset (left): time evolution of the adaptive cutoff $\tau(t)$. (c) Subcritical regime with fixed cutoff $\tau$. Inset (left): time evolution of the adaptive number of channels $N(t)$.
• Figure 5: (a) Cutoff control: time-averaged delay and fidelity (left) and standard deviation of the cutoff signal $\tau(t)$ (right) as functions of the feedback gain $\kappa_{\tau}.$ (b) Resource scaling: time-averaged delay and fidelity (left) and standard deviation of the channel allocation $N(t)$ (right) as functions of the feedback gain$\kappa_{N}$.