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arXiv:2504.11670

Adaptive Entanglement Distillation

Sijie Cheng, Narayanan Rengaswamy

Published Apr 15, 2025• 0 citations
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Abstract

Quantum network applications impose a variety of requirements on entanglement resources in terms of rate, fidelity, latency, and more. The repeaters in the quantum network must combine good methods for entanglement generation, effective entanglement distillation, and smart routing protocols to satisfy these application requirements. In this work, we focus on entanglement distillation in a linear chain of quantum repeaters. While conventional approaches reuse the same distillation scheme over multiple hop lengths after entanglement swaps, we propose a novel adaptive quantum error correction (QEC) scheme that boosts end-to-end metrics. Specifically, depending on the network operating point, we adapt the code used in distillation over successive rounds to monotonically increase the rate while also improving fidelity. We demonstrate the effectiveness of this strategy using three codes, with parameters [[9,1,3]], [[9,2,3]], [[9,3,3]], and a new performance metric, efficiency, that incorporates both overall rate and fidelity. Since the minimum input fidelity for QEC-based distillation is high, we then extend our study to include non-QEC-based purification protocols, specifically DEJMPS since it outperforms others. We compare the performance of end-to-end DEJMPS against adapting from DEJMPS to QEC once DEJMPS improves the initial fidelity to the threshold for QEC. Through a refined efficiency metric, we illuminate the regime where QEC is beneficial. These results provide a detailed outlook for entanglement purification and distillation in first and second generation quantum repeaters.

DOI
10.48550/arxiv.2504.11670

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Quantum network applications impose a variety of requirements on entanglement resources in terms of rate, fidelity, latency, and more. The repeaters in the quantum network must combine good methods for entanglement generation, effective entanglement distillation, and smart routing protocols to satisfy these application requirements. In this work, we focus on entanglement distillation in a linear chain of quantum repeaters. While conventional approaches reuse the same distillation scheme over multiple hop lengths after entanglement swaps, we propose a novel adaptive quantum error correction (QEC) scheme that boosts end-to-end metrics. Specifically, depending on the network operating point, we adapt the code used in distillation over successive rounds to monotonically increase the rate while also improving fidelity. We demonstrate the effectiveness of this strategy using three codes, with parameters [[9,1,3]], [[9,2,3]], [[9,3,3]], and a new performance metric, efficiency, that incorporates both overall rate and fidelity. Since the minimum input fidelity for QEC-based distillation is high, we then extend our study to include non-QEC-based purification protocols, specifically DEJMPS since it outperforms others. We compare the performance of end-to-end DEJMPS against adapting from DEJMPS to QEC once DEJMPS improves the initial fidelity to the threshold for QEC. Through a refined efficiency metric, we illuminate the regime where QEC is beneficial. These results provide a detailed outlook for entanglement purification and distillation in first and second generation quantum repeaters.
Efficient entanglement distribution is a cornerstone of the Quantum Internet. However, physical link parameters such as photon loss, memory coherence time, and gate error rates fluctuate dynamically, rendering static purification strategies suboptimal. In this paper, we propose an Adaptive Purification Controller (APC) that automatically optimizes the entanglement distillation sequence to maximize the goodput, i.e., the rate of delivered pairs meeting a strict fidelity threshold. By treating protocol selection as a resource allocation problem, the APC dynamically switches between purification depths and protocols (BBPSSW vs. DEJMPS) to navigate the trade-off between generation rate and state quality. Using a dynamic programming planner with Pareto pruning, simulation results show that our approach mitigates the "fidelity cliffs" inherent in static protocols and reduces resource wastage in high-noise regimes. Furthermore, we extend the controller to heterogeneous scenarios, and evaluate it for both multipartite GHZ state generation and continuous-variable systems using effective noiseless linear amplification models. We benchmark its computational overhead, showing decision latencies in the millisecond range per link in our implementation.
Entanglement distillation and entanglement swapping have been extensively studied assuming perfect quantum memories. However, near-term quantum networks will be fundamentally limited by quantum memories with a finite coherence time, resulting in complex choices for the timing and ordering of these operations. In this work, we study entanglement distillation and entanglement swapping at the level of the elementary building blocks of noisy quantum repeater networks, with the goal of elucidating the fundamental tradeoffs induced by memory decoherence. First, we focus on a minimal one-hop setting, where we analytically compare ``distill-as-soon-as-possible'' and ``distill-as-late-as-possible'' strategies against a baseline strategy that simply discards the older entangled state. We find that in the low memory coherence time regime, discarding the older entangled state achieves higher expected output fidelity, while in the high coherence time regime, delaying distillation until the end achieves the highest expected output fidelity and, over most of the deadline range, the highest weighted coherent information, at the expense of a lower success probability. We then extend our analysis to two-hop repeater chains using Monte Carlo simulation. In this setting, we find that the highest weighted coherent information is achieved by strategies that defer distillation to the end of the time window, with \textsf{Distill-ALAP-then-Swap-ALAP} and \textsf{Swap-ASAP-then-Distill-ALAP} leading at different operating points, while \textsf{Discard-Oldest-then-Swap} never reaches positive weighted coherent information in any regime tested. Together, these results clarify how decoherence reshapes the optimal operation timing in quantum networks and provide instructive insights into the link-level principles that govern larger-scale architectures.
Bell-state measurement (BSM) on entangled states shared between quantum repeaters is the fundamental operation used to route entanglement in quantum networks. Performing BSMs on Werner states shared between repeaters leads to exponential decay in the fidelity of the end-to-end Werner state with the number of repeaters, necessitating entanglement distillation. In this work, we use quantum error correcting codes for deterministic entanglement distillation to route Werner states on a chain of repeaters. To maximize the end-to-end distillable entanglement, we utilize global link-state knowledge to determine the optimal policy for scheduling distillation and BSMs at the repeaters. We observe that low-rate codes produce high-fidelity end-to-end states owing to their excellent error-correcting capability, whereas high-rate codes yield a larger number of end-to-end states but of lower fidelity. The number of quantum memories used at repeaters increases with the code rate as well as the classical computation time of the decoder.
Quantum repeaters are essential to realizing long-range entanglement distribution networks. To achieve enhanced rates of high-fidelity entanglement distribution, we investigate how entanglement distillation can be used on trapped-ion-based quantum repeater networks. Entanglement distillation is the process of distilling from a large number of copies of low-fidelity entangled qubits a fewer number of copies of higher-fidelity entangled qubits. It has been shown that quantum error-correcting codes (QECCs) can be used to devise protocols for entanglement distillation. In this paper, we consider entanglement distillation based on three lifted-product (LP) quantum low density parity check (QLPDC) codes ([[544, 80, 12], [[714, 100, 16]], and [20, 10, 136, 20]) on trapped-ion repeater networks with spatial and time multiplexing over various total distances with different inter-repeater spacing to calculate the end-to-end entanglement rates that they enable. The reported rates assume entanglement over each elementary link succeeds synchronously and do not assume any constraint on the number of ions present in each trap. We furthermore assume that distillation occurs at every elementary link and that the entanglement swaps are ideal. Our findings can be considered as groundwork for implementing more efficient distillation and communication protocols on trapped ion networks.
Future quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation strategies for long-distance entanglement distribution. In this work, we focus on quasi-local policies for multiplexed quantum repeater chains. In fully-local policies, nodes use the knowledge of only their own states, whereas more efficient global policies use knowledge of the entire network state. The classical communication costs of using this knowledge have not been explored in existing literature. We show that quasi-local policies not only obtain improved performance over local policies, but also reduce classical communication costs considerably. Our policies also outperform the widely studied nested purification and doubling policy in practical parameter regimes. We identify parameter regimes where distillation is useful and address the question: “Should we distill before swapping, or vice versa?” Finally, we propose an implementation scheme for a multiplexed repeater chain, experimentally demonstrate the key element, a high-dimensional biphoton frequency comb, and evaluate its anticipated performance using our multiplexing-based policies. Fast and reliable entanglement distribution in quantum networks requires multiplexing to enhance rates and distillation to compensate the loss in fidelity. Classical communication latency associated with both swapping and distillation protocols is a significant hurdle, which the authors address by proposing a class of quasi-local entanglement distribution policies for multiplexed repeater chains.
It is crucial to share maximally entangled pairs in quantum information processing. However, unwanted interactions with the environment can reduce the entanglement fidelity of the produced pairs. Entanglement distillation is a method to overcome this problem by creating higher-fidelity entangled pairs from a more significant number of lower-fidelity pairs. This study uses Werner states and imperfect gates to analyse the performance of BBPSSW, DEJMPS, 3-to-1, and EPL protocols for entanglement distillation. Specifically, this study focuses on how the increase in fidelity depends on the input pair and gate fidelities. The results are obtained through numerical simulation using the NetSquid simulator. After characterising the numerical errors, the study demonstrates that all four protocols increase the pair fidelity for a gate higher than 0.96. The study also reveals that the higher the success fidelity, the lower the probability, as predicted theoretically. Additionally, based on a list of requirements and hardware performance, we developed a simple recipe for selecting the most suitable protocol. The simulation results highlight the practical limitations of entanglement distillation protocols, indicating the need for further investigation. This includes the development of a theoretical model for the EPL protocol implemented with Werner states, incorporating noisy measurements in the simulated protocols and increasing the number of simulations for higher accuracy.