Practical Routing and Criticality in Large-Scale Quantum Communication Networks

TL;DR

The paper addresses how to design large-scale quantum communication networks to guarantee high end-to-end rates under realistic, noisy optical-fiber conditions. It combines random network models (Waxman and scale-free) with practical edge models (bosonic thermal-loss channels and CV-QKD) and introduces efficient multi-path routing (IAR-MDPAlg) to overcome single-path limitations. Key contributions include a formal framework for end-to-end performance and routing consumption, definitions of performance- and consumption-based network criticality, and numerical demonstrations that multi-path routing dramatically lowers the required nodal density for reliable communication. The findings have practical impact by guiding the design of scalable quantum networks, showing that multi-path routing, rather than flooding or solely relying on connectivity, is essential for achieving robust quantum communication with feasible resource costs; the results also reveal how network architecture (Waxman vs scale-free) strongly mediates these outcomes.

Abstract

The efficacy of a communication network hinges upon both its physical architecture and the protocols that are employed within it. In the context of quantum communications, there exists a fundamental rate-loss tradeoff for point-to-point quantum channels such that the rate for distributing entanglement, secret keys, or quantum states decays exponentially with respect to transmission distance. Quantum networks are the solution to overcome point-to-point limitations, but they simultaneously invite a challenging open question: How should quantum networks be designed to effectively and efficiently guarantee high rates? Now that performance and physical topology are inexorably linked, this question is not easy, but the answer is essential for a future quantum internet to be successful. In this work, we offer crucial insight into this open question for complex optical-fiber quantum networks. Using realistic descriptions of quantum networks via random network models and practical end-to-end routing protocols, we reveal critical phenomena associated with large-scale quantum networks. Our work reveals the weaknesses of applying single-path routing protocols within quantum networks, observing an inability to achieve reliable rates over long distances. Adapting novel algorithms for multi-path routing, we employ an efficient and practical multi-path routing algorithm capable of boosting performance while minimizing costly quantum resources.

Figures (8)

• Figure 1: Connectivity properties of bosonic thermal-loss Waxman networks. Panel (a) displays random networks generated under the parameters listed above and using single-edge capacity upper-bounds. The colour intensity of each edge is proportional to its capacity. Panel (b) plots the average main component fraction, in which the critical densities necessary for a connectivity phase transition are identified by the black lines. Panel (c) shows the average degree of networks with a fixed number of nodes (given in legend) with respect to variable network density and area respectively. The legend identifies the fixed node number and indicates whether the network uses upper or lower bounds on the rate distributions.
• Figure 2: Connectivity properties of bosonic thermal-loss scale-free networks. Panel (a) displays random networks generated under the parameters listed above and using single-edge capacity upper-bounds. The opacity of each edge is proportional to its capacity. Panel (b) plots the average giant component fraction and (c) the average degree of networks with a fixed number of nodes with respect to variable network density and area respectively. The legend identifies the fixed node number and $\sigma$ exponent.
• Figure 3: Relationships between performance, routing consumption and nodal density in bosonic thermal-loss Waxman networks. The network link layer in all cases is described by the upper-bound capacity distribution $\mathcal{K}_u$ from Eq. (\ref{['eq:RD_u']}) and model parameters $(r_0, \beta) = (100,1)$. Panels (a)-(b) plot the ensemble average end-to-end capacities achieved by different routing protocols and a number of network radii, $R$ (each protocol and network radius is colour coded with the routing protocol and $R$ legends). Panels (c)-(d) show the ensemble average routing consumption of (c) single path routing and (d) $\mathcal{P}_{\text{mdp}}^{R^{\star}=1}$ routing via the IAR-MDPAlg. Panel (e) depicts achievable end-to-end routes on an example network (according to the parameters listed) using $\mathcal{P}_{\text{sp}}$ and $\mathcal{P}_{\text{mdp}}^{R^{\star}=1}$ for users separated by $r_{\boldsymbol{i}} \approx 800$ km. Black edges in the networks identify unused edges, while red edges are those which engage in the routing protocol.
• Figure 4: Waxman quantum network phase characterisations with respect to link layer descriptions and nodal density. Panel (a) outlines connectivity, consumption and performance based critical densities with respect to networks composed of different link layers. These transitions give rise to network phases in which we can expect particular properties. These phases are labelled on the density diagram, while Panel (b) summarises and describes their implications for quantum networking. Phases III and V describe similar network properties, but differ as to whether the maximum routing consumption is surpassed before or after the flooding-based performance transition. Note that Phase III appears in networks described by the thermal upper-bound capacity distribution, while Phase V appears in the lower-bound capacity distribution.
• Figure 5: Relationships between performance, routing consumption and nodal density in bosonic thermal-loss scale-free networks. Throughout all plots, the network link layer is described by the upper-bound capacity distribution $\mathcal{K}_u$ from Eq. (\ref{['eq:RD_u']}) and we use the model parameters $(n_0, m, \sigma_{\text{deg}}) = (10,5,1)$. We also consider unique values for the scale-free model parameter $\sigma_r \in \{1,2\}$ which are distinguished in the legend. Panels (a)-(c) depict the ensemble average capacity with respect to nodal density for $\mathcal{P}_{\text{fl}}$, $\mathcal{P}_{\text{sp}}$ and $\mathcal{P}_{\text{mdp}}^{{R}^{\star}=1}$ routing respectively. Panels (d)-(e) plot the ensemble average routing consumption with respect to nodal density for $\mathcal{P}_{\text{sp}}$ and $\mathcal{P}_{\text{mdp}}^{{R}^{\star}=1}$ routing respectively. Each analysis is performed for a number of network radii $R$ listed in the legend. Panel (f) illustrates achievable end-to-end routes on an example network (under the parameters shown) using $\mathcal{P}_{\text{sp}}$ and $\mathcal{P}_{\text{mdp}}^{R^{\star}=1}$ for users separated by $r_{\boldsymbol{i}} \approx 200$ km. Black edges in the networks identify unused edges, while red edges are those which engage in the routing protocol.

Theorems & Definitions (3)

• Definition 1
• Definition 2
• Definition 3