From Entanglement Purification Scheduling to Fidelity-Constrained Entanglement Routing

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 singlehop case and analyze the 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 polynomialtime algorithm constructing an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\epsilon$</tex>-optimal fidelity-constrained path. The effectiveness of our algorithms are also numerically demonstrated by extensive simulations.