From Entanglement Purification Scheduling to Fidelity-constrained Multi-Flow Routing

TL;DR

This paper addresses key challenges in quantum networking by developing algorithms for optimal entanglement purification scheduling and fidelity-constrained path routing, enhancing quantum network reliability.

Contribution

It introduces the first optimal scheduling algorithm for single-hop entanglement purification and a polynomial-time method for fidelity-constrained path routing.

Findings

Optimal purification scheduling for single-hop cases.

Closed-form condition for multi-hop purify-and-swap strategy.

Efficient algorithms for fidelity-constrained path construction.

Abstract

Recently emerged as a disruptive networking paradigm, quantum networks rely on the mysterious quantum entanglement to teleport qubits without physically transferring quantum particles. However, the state of quantum systems is extremely fragile due to environment noise. A promising technique to combat against quantum decoherence is entanglement purification. To fully exploit its benefit, two fundamental research questions need to be answered: (1) given an entanglement path, what is the optimal entanglement purification schedule? (2) how to compute min-cost end-to-end entanglement paths subject to fidelity constraint? In this paper, we give algorithmic solutions to both questions. For the first question, we develop an optimal entanglement purification scheduling algorithm for the single-hop case and analyze the \textsc{purify-and-swap} strategy in the multi-hop case by establishing the closed-form condition for its optimality. For the second question, we design a polynomial-time algorithm constructing an $\epsilon$-optimal fidelity-constrained path. The effectiveness of our algorithms are also numerically demonstrated by extensive simulations.