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.
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.
We recently proposed an entanglement distillation protocol based on local operations and classical communication that probabilistically and universally distills a maximally entangled Bell pair from multiple copies of an unknown two-qubit state [Phys. Rev. Lett. 135, 260202 (2025)]. Here, we investigate the robustness of this protocol against imperfections in its implementation. We consider several incoherent and coherent gate-error models, as well as measurement readout errors, and determine the regimes in which distillation enhances the fidelity with the target Bell state. We find that the protocol remains effective over substantial error ranges, although its robustness depends strongly on the type of error. We further analyze asymmetric errors between the two parties and identify conditions under which complementary postselection outcomes yield identical distillation dynamics, allowing the success probability to be enhanced.
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.
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.
Near-term and early fault-tolerant quantum computing architectures are expected to exhibit highly non-uniform error rates. In particular, local operations within a chip can be substantially more reliable than operations connecting different chips or dilution refrigerators. Such inter-module operations can therefore become a dominant bottleneck, even when quantum error correction is applied. Entanglement distillation provides a natural way to trade additional operations and qubits for higher-fidelity entanglement. Standard distillation protocols, however, are usually formulated in an LOCC resource model, in which several noisy Bell pairs are generated initially and all subsequent processing consists only of local operations and classical communication. Here, we consider a generalized model tailored to modular quantum computing hardware, in which the two modules have access to high-fidelity local operations and to repeated uses of the same noisy inter-module entangling operation during the protocol. We develop practical small-scale entanglement distillation protocols designed to minimize both space and time overhead. Remarkably, our main protocol requires only two qubits per module, yet achieves quadratic error suppression of inter-module errors, assuming local operations are much cleaner. Compared with existing small-scale protocols, our space-optimal protocol provides more space- and time-efficient quadratic error suppression and achieves the best performance in our simulations and experiments on noisy links of current superconducting quantum processors. These results suggest that inter-module-gate-assisted entanglement distillation can be a practical primitive for overcoming noisy links in modular quantum computing architectures.
High-fidelity entanglement shared between distant quantum systems is an essential resource for quantum communication and computation. Entanglement distillation addresses this need by converting multiple noisy Bell pairs into fewer higher-fidelity pairs, using only local quantum operations and classical communication. However, this approach typically requires a substantial overhead in the number of qubits. To bypass this hurdle, we propose to leverage the high-dimensional Hilbert space of a single pair of bosonic systems to store a large amount of entanglement, replacing the need for multi-qubit systems. To distill entanglement in such a setup, we devise a new entanglement distillation protocol, tailored for bosonic systems. The protocol converts a highly-entangled noisy state between two bosonic systems into a lower-dimensional but high-fidelity entangled state, using only local bosonic operations. We show that our protocol significantly enhances the fidelity of the entangled state in the presence of naturally occurring loss and dephasing errors. Compared to methods relying on multiple Bell pairs, our scheme offers a more hardware-efficient strategy, providing a practical route toward the realization of entanglement distillation.
Uncontrolled interactions with the environment introduce errors that remain a significant challenge to the reliability of quantum technologies using entanglement. An essential method to overcome or mitigate these errors is entanglement distillation, the transformation of multiple copies of weakly entangled states into a smaller number of approximately maximally entangled states. We present a comparative analysis of the distillation effectivity for the stabilizer-based two-copy entanglement distillation protocol, FIMAX, against other recurrent two-copy protocols, including ADGJ, DEJMPS, P1–P2 and the generalized BBPSSW protocol. We focus on low-fidelity bipartite quantum states in dimensions [Formula: see text] and [Formula: see text], which are particularly challenging to distill. Our findings demonstrate that FIMAX exhibits superior performance regarding the distillable share for these states. While other protocols struggle with highly noisy states, FIMAX successfully distills entanglement even when the initial state quality is severely compromised. These results highlight the protocol’s capability to address the effects of environmental noise, advancing the robustness and scalability of quantum technologies leveraging entanglement distillation.