Entanglement Purification With Finite Latency Classical Communication in Quantum Networks

Quantum networks rely on high fidelity entangled pairs distributed to nodes, but maintaining their fidelity is challenged by environmental decoherence during storage. Entanglement purification is used to restore fidelity, but the idle periods imposed by the associated classical communication delays counteract this goal by exposing the states to further decoherence. In this work, we analyze the practical viability of entanglement purification protocols (BBPSSW, DEJMPS), under non-instantaneous classical coordination over Internet protocol (IP) communications networks. We present a comprehensive performance evaluation of these protocols in various network conditions for a range of quantum memory technologies. We employ a microscopic Lindblad treatment of the underlying quantum dynamics, and use current-generation metropolitan IP network latency statistics and parameters drawn from quantum memory testbeds. In doing so we identify the regions in which entanglement purification succeeds and fails, delineated by break-even iso-fidelity contours in the phase space. We then determine the total number of entangled pairs required to complete a multi-round purification protocol, and the steady-state throughput of entangled pairs with purified fidelities that exceed application-specific thresholds. This provides latency budgets, memory quality targets, and resource-overhead estimates for deploying purification on current and near-future networks.