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arXiv:2607.21555

Enhancing Entanglement Purification with Shared Randomness

Allen Zang, Bikun Li, Xinan Chen, Eric Chitambar, Liang Jiang, Martin Suchara, Tian Zhong

quant-phSubmitted Jul 23, 2026• Announced Jul 24, 2026• 0 citations
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Abstract

Entanglement purification protocols (EPPs) are essential for improving entanglement fidelity to support fault-tolerant distributed quantum information processing. Practical entanglement sources are often heterogeneous and source labels may be unavailable at the EPP layer. We show that classical shared randomness, together with buffer memories, can enhance entanglement purification when source labels are unavailable, without state characterization or EPP circuit optimization. The strategy is to accumulate multiple entanglement distribution rounds and then use shared randomness to shuffle all the stored entangled states before packaging them as inputs to the EPP. For any $n$ Werner sources and any fixed $n$-to-1 bilocal Clifford EPP, we prove that accumulating and shuffling improves the expected success probability and the success-weighted output Bell fidelity over the baseline without accumulating and shuffling, for every $n$, for every finite number of accumulation rounds and in the asymptotic limit, and the improvement increases monotonically with the number of accumulation rounds.

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32 pages, 3 figures

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Entanglement purification protocols (EPPs) are essential for improving entanglement fidelity to support fault-tolerant distributed quantum information processing. Practical entanglement sources are often heterogeneous and source labels may be unavailable at the EPP layer. We show that classical shared randomness, together with buffer memories, can enhance entanglement purification when source labels are unavailable, without state characterization or EPP circuit optimization. The strategy is to accumulate multiple entanglement distribution rounds and then use shared randomness to shuffle all the stored entangled states before packaging them as inputs to the EPP. For any nnn Werner sources and any fixed nnn-to-1 bilocal Clifford EPP, we prove that accumulating and shuffling improves the expected success probability and the success-weighted output Bell fidelity over the baseline without accumulating and shuffling, for every nnn, for every finite number of accumulation rounds and in the asymptotic limit, and the improvement increases monotonically with the number of accumulation rounds.
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While the concept of entanglement purification protocols (EPPs) is straightforward, the integration of EPPs in network architectures requires careful performance evaluations and optimizations that take into account realistic conditions and imperfections, especially probabilistic entanglement generation and quantum memory decoherence. It is important to understand what is guaranteed to be improved from successful EPP with arbitrary non-identical input, which determines whether we want to perform the EPP at all. When successful EPP can offer improvement, the time to perform the EPP should also be optimized to maximize the improvement. In this work, we study the guaranteed improvement and optimal time for the CNOT-based recurrence EPP, previously shown to be optimal in various scenarios. We firstly prove guaranteed improvement for multiple figures of merit, including fidelity and several entanglement measures when compared to practical baselines as functions of input states. However, it is noteworthy that the guaranteed improvement we prove does not imply the universality of the EPP as introduced in arXiv:2407.21760. Then we prove robust, parameter-independent optimal time for typical error models and figures of merit. We further explore memory decoherence described by continuous-time Pauli channels, and demonstrate the phenomenon of optimal time transition when the memory decoherence error pattern changes. Our work deepens the understanding of EPP performance in realistic scenarios and offers insights into optimizing quantum networks that integrate EPPs.
An entanglement purification protocol (EPP) aims to transform multiple noisy entangled states into a single entangled state with higher fidelity. In this work we consider input-independent EPPs that always yield an output fidelity no worse than each of the original noisy states, a property we call universality. We prove there is no n-to-1 EPP implementable by local operations and classical communication that is universal for all two-qubit entangled states, whereas such an EPP is possible using more general positive partial transpose-preserving (PPT) operations. We also show that universality is impossible by any bilocal Clifford EPP even when restricted to states with fidelities above an arbitrarily high threshold.
Entanglement purification is an indispensable ingredient in extended quantum communication networks and usually determines the efficiency and communication rate of quantum communication protocols. Different from all existing entanglement purification protocols (EPPs) where two or more copies of low quality mixed entangled states are selected from the same ensemble, here we describe a general and optimal EPP for arbitrary initial mixed states from different ensembles. We show that the successful operation of EPP may not obtain a higher fidelity mixed state, while the discarded source pair, which is usually regarded as a failure in existing EPPs, may have residual entanglement and can be reused to increase the yield of entanglement purification. We give the criterions of both the successful purification to obtain a higher fidelity mixed state and the existence of residual entanglement. Moreover, we reveal that entanglement purification procedure causes some entanglement loss. Finally, we provide an optimal approach to reduce the entanglement loss. This approach can also be used to increase the yield of entanglement purification. Our EPP may have potential application in long-distance quantum communications.
Noise and photon loss encountered on quantum channels pose a major challenge for reliable entanglement generation in quantum networks. In near-term networks, heralding is required to inform endpoints of successfully generated entanglement. If after heralding, entanglement fidelity is too low, entanglement purification may be utilized to probabilistically increase fidelity. Traditionally, purification protocols proceed as follows: generate heralded EPR pairs, execute a series of quantum operations on two or more pairs between two nodes, and classically communicate results to check for success. Purification may require several rounds while qubits are stored in memories, vulnerable to decoherence. In this work, we explore notions of optimistic purification, wherein classical communication required for heralding and purification is delayed, possibly to the end of the process. Optimism reduces the overall time EPR pairs are stored in memory, increasing fidelity while possibly decreasing EPR pair rate due to decreased heralding and purification failure. We apply optimism to the entanglement pumping scheme, ground- and satellite-based EPR generation sources, and current state-of-the-art purification circuits that include several measurement and purification checkpoints. We evaluate performance in view of a number of parameters, including link length, EPR source rate and fidelity; and memory coherence time. We show that while our optimistic protocol increases fidelity, the traditional approach may even decrease fidelity for longer distances. We study the trade-off between rate and fidelity under entanglement-based QKD, and find that optimistic schemes can yield higher rates compared to non-optimistic counterparts, with most advantages seen in scenarios with low initial fidelity and short coherence times.
Entanglement generation over large distances is a challenging task due to photon loss, which grows exponentially with link length (e.g., optical fiber). Moreover, EPR pair generation over noisy channels results in imperfect states. Thus, a link is associated with a success probability and an initial fidelity for successfully-generated entanglement. Over time, fidelity de-creases due to environmental noise. Entanglement purification is a way of probabilistically increasing state fidelity. Traditionally, purification protocols perform the following steps: generate two or more EPR pairs between two nodes, execute a series of quantum gates on both sides, and exchange results via classical messages. In this work, we propose a twist on the original entanglement pumping scheme, wherein a fixed number of purification steps are performed successively, before the classical information exchange. This modification introduces optimism to the overall procedure, such that classical communication is performed only at the end, to check the measurement results. The protocol is also optimistic about entanglement generation and does not wait for heralding signals before attempting purification. We study the effect of being optimistic on fidelity and the waiting time to generate an entangled pair as a function of the distance between network nodes. We observe an improvement in both fidelity and expected waiting time. We also study the effect of the number of purification steps on fidelity and latency and observe that typically no more than two or three purification steps are needed when limited by only two memories.