Swapping and purification are the two fundamental building blocks for multi-hop quantum networks. However, their interplay and its impact on end-to-end fidelity and cost are not yet fully explored. Existing scheduling algorithms address this problem under certain simplified assumptions and models that may not fully capture the complexities of real scenarios. In this work, we first consider more general assumptions that account for operation failures and extend a tree-based modeling approach for joint swapping and purification. Then, for the first time, we analytically prove the previous conjecture that the optimal strategy under Binary system is always to purify the entanglements before any swapping. This sheds light on the protocol and device design for entanglement distribution in quantum networks. We then further propose a tree-based algorithm, which can efficiently schedule swapping and purification along a path for both Binary and Werner systems. Extensive simulations have been conducted to evaluate the proposed method against the existing solutions, and the results show that our method uses fewer entanglements to establish qualified end-to-end entanglements and thus achieves higher network throughput.
Swapping and purification are the two fundamental building blocks for high-fidelity entanglement distribution in multi-hop quantum networks. Unfortunately, it is still a mystery how they intertwine with each other to affect the fidelity and cost of end-to-end entanglements. Current scheduling algorithms consider this problem under relatively limited assumptions and a critical yet unjustified conjecture. In this work, we first consider more general assumptions with operation failures and, accordingly, extend a tree-based modeling for joint swapping and purification. Then, we analytically prove the previous conjecture that the optimal strategy underBinary systemis always to purify the entanglements before any swapping. This sheds light on the protocol and device design for quantum networks. We then further propose a tree-based algorithm, which can efficiently schedule swapping and purification along a path for bothBinaryandWerner systems. Extensive simulations of the proposed method against state-of-the-art solutions show that our method uses fewer entanglements to establish qualified end-to-end entanglements, and thus achieves higher network throughput.
Entanglement purification with two entangled resource pairs is widely employed in the literature on quantum repeater networks to counteract fidelity degradation introduced by noisy quantum memories and entanglement swapping across multiple hops. Standard purification protocols assume both resource pairs carry identical fidelity. In practice, entanglement generation is stochastic, the two resource pairs are heralded at different times, and so the first pair decoheres in memory while the second is being generated. Thus a fidelity asymmetry is a structural feature of any network operating under realistic memory conditions, leading to the question: when is it beneficial to perform purification? We derive a closed-form fidelity asymmetry tolerance delta(F) that governs whether a purification attempt is beneficial. We determine a universal upper bound delta_max of approximately 0.076 beyond which purification is always counterproductive. Our simulations show that with exponential memory decoherence, purification yields benefits in only approximately 14% of purification attempts on two resource pairs in a two-hop repeater chain. We define three network objectives: fidelity only, time only, and a combination of time and fidelity, to deliver end-to-end entanglement. We show that when the application fidelity requirement is achievable through swapping alone, no-purification is the superior policy, with its advantage increasing with the number of hops. When the fidelity requirement cannot be met with swapping alone and purification is necessary, to be effective, it must be conditioned on delta(F) between resource pairs. We introduce DeltaPurify, a policy that conditions purification decisions on local fidelity information, and show it reduces time-to-serve relative to both naive purification and no-purification across several fidelity thresholds and hops of a repeater chain.
Quantum data-center networks must distribute entanglement between QPUs over paths whose length grows with system scale, but each entanglement-swapping step reduces the quality of the raw end-to-end state. Topology, multiplexing, and repeated connection attempts can increase the number of raw end-to-end copies available for a request, yet they do not answer the central resource question: whether those copies are sufficient to remove, via entanglement purification, the fidelity loss caused by multi-hop distribution. We study this question through a topology-independent black-box model of the network. Each elementary link is modeled as a Werner state with parameter
w0, so ideal swapping over an
ℓ-link path produces equal-quality raw copies with Werner parameter
w0ℓ; purification succeeds if it outputs at least one state with Werner parameter at least
w0 with probability at least
pth. We compare recursive BBPSSW purification with higher-order
r-to-
1 bilocal-Clifford purification protocols of Jansen \emph{et al.}, using an all-in recursive schedule whose success probability is computed by exact dynamic programming. The resulting resource landscapes show a threshold structure governed by the Werner entanglement condition
w0ℓ>1/3 and demonstrate that multi-copy purification substantially improves both feasibility and copy efficiency. Across the evaluated grid, the Jansen family requires fewer copies than BBPSSW at more than
96% of shared feasible points; at
pth=0.70, the median copy budget drops from
268 to
30. These results provide a quantitative purification-resource benchmark for assessing whether future quantum data-center architectures can practically support hop-independent end-to-end entanglement quality.
Quantum networks rely on the efficient distribution of entanglement to enable long-distance quantum communication and information processing. A key challenge in these networks is the design of routing protocols capable of maintaining high quality entanglement in the presence of noise, decoherence, and imperfect operations, which progressively degrade the fidelity of entangled states through entanglement swapping. Entanglement purification provides an effective mechanism to mitigate this degradation at the cost of additional resources. In this work, we study purification-aware quantum routing and formulate the problem of selecting optimal purification strategies as an optimization task. By employing dynamic programming techniques, we identify strategies that optimally balance resource consumption and end-to-end fidelity, demonstrating the effectiveness of our approach across different scenarios.