On Selecting Paths for End-to-End Entanglement Creation in Quantum Networks

TL;DR

This work investigates routing for end-to-end entanglement in quantum networks under realistic constraints, showing that pre-existing entanglements from prior cycles can alter the optimal path. It develops a case study contrasting a clean-slate 2-hop path with a 4-hop path that leverages prior entanglements, using an SDN controller and a depolarizing noise model to capture probabilistic generation, swapping, and memory decoherence. Key contributions include identifying a 4-hop favorable regime at low $p_e$ and high $p_s$, introducing entanglement diversity with first-completion and all-completion strategies, and analyzing trade-offs between cutoff time and fidelity. The findings emphasize the importance of incorporating prior entanglements and fidelity decay into routing decisions, offering practical guidelines for path selection and strategies like distillation to improve end-to-end entanglement rates in realistic quantum networks.

Abstract

Optimal routing is a fundamental challenge in quantum networking, with several approaches proposed to identify the most efficient path for end-to-end (e2e) entanglement generation between pairs of nodes. In this paper, we show that \textit{prior entanglements} -- entanglements generated in a previous network cycle but not yet utilized -- are an important consideration in optimal path selection due to the dynamic nature of quantum networks. Specifically, we investigate whether a longer path with pre-existing entanglements can outperform a shorter path that starts from scratch. We account for key quantum constraints, including noisy entanglement generation and swapping, fidelity decay, probabilistic operations, and link discarding upon swap failure. Simulations reveal that longer paths with prior entanglements can establish e2e entanglement faster than shorter paths under certain conditions. We further introduce the notion of \textit{entanglement diversity}, where multiple paths can be used to improve performance -- either by selecting the first successful path to minimize time or using both paths to enhance fidelity through distillation. These findings highlight the importance of incorporating prior entanglements into path selection strategies for optimizing quantum communication networks.

Figures (9)

• Figure 1: An entanglement swap performed between entangled pairs of nodes 1-2 and 2-3. A BSM is performed at the intermediate node (node 2), resulting in the connection of nodes 1 and 3 without requiring direct interaction between them
• Figure 2: Network of $n=10$ nodes and an SDN controller
• Figure 3: Path with four hops with partial entanglements between nodes 1-2 and 3-5
• Figure 4: Sequential swaps
• Figure 5: CDF of the number of time steps required for e2e entanglement generation for various values of $p_e$ and $p_s$ with $T$ = 5