Distribution and Purification of Entanglement States in Quantum Networks

TL;DR

The paper tackles distributing high fidelity entanglement in quantum networks under a fidelity threshold by integrating purification with entanglement swapping and fusion. It develops a DP framework for optimal purification-augmented swapping trees (EDP) and an LP-based hypergraph flow for concurrent purification-augmented structures (GEDP), then extends these ideas to GHZ state distribution with GDP and GGDP, including practical approximations to manage exponential state growth. The approaches are demonstrated via NetSquid simulations, showing substantial improvements over prior heuristic methods inEP and GHZ generation rates. The work provides scalable, fidelity-guaranteed strategies for practical quantum networking and offers a pathway to generalize to other graph states and quantity-based performance models.

Abstract

We consider problems of distributing high-fidelity entangled states across nodes of a quantum network. We consider a repeater-based network architecture with entanglement swapping (fusion) operations for generating long-distance entanglements, and purification operations that produce high-fidelity states from several lower-fidelity states. The contributions of this paper are two-fold: First, while there have been several works on fidelity-aware routing and incorporating purification into routing for generating EPs, this paper presents the first algorithms for optimal solutions to the high-fidelity EP distribution problem. We provide a dynamic programming algorithm for generating the optimal tree of operations to produce a high-fidelity EP, and an LP-based algorithm for generating an optimal collection of trees. Second, following the EP algorithms, this paper presents the first algorithms for the high-fidelity GHZ-state distribution problem and characterizes its optimality. We evaluate our techniques via simulations over NetSquid, a quantum network simulator.

Figures (8)

• Figure 1: (a) Entanglement swapping over the triplet of nodes $(A, B, C)$, which results in $A$'s qubit entangled with $C$'s qubit. (b) Purification of entanglement (blue, middle) using sacrificial EP (red, top), resulting in a higher-fidelity EP (blue, bottom) if the operation is successful.
• Figure 2: A purification-augmented swapping tree over a path. Binary internal nodes perform entanglement swapping, and unary nodes do purification. The leaves of the tree generate link EPs and internal nodes generate remote EPs.
• Figure 3: Example level-based fusion structure. This "aggregates" of two purification-augmented swapping trees. For illustration, the figure assumes that a parent's generation rate is 1/3 of the rate of its children for swapping and 1/2 for purification. The leaf node $(x_0, x_1)$'s generation rate of 36 units is "split" into 9 and 27 for the two different (red and blue) swapping operations. The two root nodes represent the final/target EP formed in two different ways---for a total generation rate of 6 (3 from each swapping operation). Unary nodes represent the results of purification operations.
• Figure 4: The first stage of the distribution of GHZ states: the generation of virtual links between terminal nodes. (a) The quantum network and terminal nodes of the GHZ state. (b) The virtual links generated for the star-graph approach.
• Figure 5: Generation Rates for EPs for various schemes, for varying parameter values, from NetSquid simulations.