Routing and Spectrum Allocation in Broadband Quantum Entanglement Distribution

TL;DR

The paper tackles routing and spectrum allocation for repeaterless broadband quantum entanglement distribution using a single broadband EPR-pair source in a source-in-the-middle configuration. It develops a polynomial-time optimal routing method via Suurballe’s algorithm and analyzes max-min fair spectrum allocation through several approximations, identifying BD and modified LPT as strong performers under multiple metrics. Through extensive simulations on an ILEC Manhattan topology and Watts-Strogatz networks, the work reveals tradeoffs between minimum-rate fairness, median performance, Jain fairness, and computational burden, and shows that source placement significantly influences outcomes. The results provide actionable guidance for near-term quantum network deployments and highlight directions for scalability and multi-source extensions.

Abstract

We investigate resource allocation for quantum entanglement distribution over an optical network. We characterize and model a network architecture that employs a single broadband quasi-deterministic time-frequency heralded Einstein-Podolsky-Rosen (EPR) pair source, and develop a routing and spectrum allocation scheme for distributing entangled photon pairs over such a network. As our setting allows separately solving the routing and spectrum allocation problems, we first find an optimal polynomial-time routing algorithm. We then employ max-min fairness criterion for spectrum allocation, which presents an NP-hard problem. Thus, we focus on approximately-optimal schemes. We compare their performance by evaluating the max-min and median number of EPR-pair rates assigned by them, and the associated Jain index. We identify two polynomial-time approximation algorithms that perform well, or better than others under these metrics. We also investigate scalability by analyzing how the network size and connectivity affect performance using Watts-Strogatz random graphs. We find that a spectrum allocation approach that achieves higher minimum EPR-pair rate can perform significantly worse when the median EPR-pair rate, Jain index, and computational resources are considered. Additionally, we evaluate the effect of the source node placement on the performance.

Figures (10)

• Figure 1: Correspondence between a network layout and its graph model. \ref{['fig:source_consumer_network_model']} shows a network of source (A) and consumer nodes (B, C, and D). \ref{['fig:source_consumer_graph_model']} shows the corresponding graph model.
• Figure 2: Rate of EPR-pair generation in $m=185$ channels, each $B_{\text{c}}=11$ GHz wide, with center frequencies separated by $B_{\Delta}=13.135$ GHz, derived from shapiro2024entanglementsourcequantummemory, used for simple and ILEC networks. The bottom-axis label shows the channel indices and the top-axis label shows the center wavelength of each channel. The highest and lowest per-channel rates are 4584.0 and 458.0 EPR pairs/s, respectively.
• Figure 3: A map of Manhattan with ILEC nodes and links overlaid. The distance matrix is given in Table \ref{['table:manhattan_distance_matrix']}.
• Figure 4: Topology of the simple network. The EPR-pair source is at Node A.
• Figure 5: Comparison of performance using different allocation strategies on the simple network depicted in Fig. \ref{['fig:simple_layout']} for 8 dB WSS loss and source node location A. In \ref{['fig:simple_results']}, we report unnormalized (left-axis label) and normalized (right-axis label) minimum EPR-pair rates received by any node pair.