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Physical Review A

Robustness of hashing protocols for entanglement purification

Michael J. Zwerger, Hans J. Briegel, Wolfgang Dür

Published Jul 10, 2014• 38 citations
Publisher

Abstract

We investigate entanglement purification protocols based on hashing, where a large number of noisy entangled pairs are jointly processed to obtain a reduced number of perfect, noiseless copies. While hashing and breeding protocols are the only purification protocols that asymptotically obtain a nonzero yield, they are not applicable in a realistic scenario if local gates and measurements are imperfect. We show that such problems can be overcome by a compact measurement-based implementation, yielding entanglement purification schemes with nonzero yield that are applicable also in noisy scenarios, with tolerable noise per particle of several percent. We also generalize these findings to multiparty purification protocols for arbitrary graph states.

DOI
10.1103/physreva.90.012314

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We investigate entanglement purification protocols based on hashing, where a large number of noisy entangled pairs are jointly processed to obtain a reduced number of perfect, noiseless copies. While hashing and breeding protocols are the only purification protocols that asymptotically obtain a nonzero yield, they are not applicable in a realistic scenario if local gates and measurements are imperfect. We show that such problems can be overcome by a compact measurement-based implementation, yielding entanglement purification schemes with nonzero yield that are applicable also in noisy scenarios, with tolerable noise per particle of several percent. We also generalize these findings to multiparty purification protocols for arbitrary graph states.
We investigate entanglement purification protocols based on hashing, where a large number of noisy entangled pairs is jointly processed to obtain a reduced number of perfect, noiseless copies. While hashing and breeding protocols are the only purification protocols that asymptotically obtain a nonzero yield, they are not applicable in a realistic scenario if local gates and measurements are imperfect. We show that such problems can be overcome by a compact measurement-based implementation, yielding entanglement purification schemes with nonzero yield that are applicable also in noisy scenarios, with tolerable noise per particle of several percent. We also generalize these findings to multiparty purification protocols for arbitrary graph states.
We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about the number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e., high fidelity of initial states. The main tool is a counter gate with which the required nonlocal information can be transferred into the high-dimensional entangled qudit auxiliary states. We compare our schemes to standard recurrence protocols that operate on pairs of copies, and hashing and breeding protocols that operate on a (asymptotically) large number of copies. Our protocols interpolate between these two regimes, leading to higher achievable fidelity and yield. We illustrate our approach for bipartite qubit states and generalize it to purify multiparty GHZ states.
We present multiparty entanglement purification protocols that are capable of purifying arbitrary graph states directly. We develop recurrence and breeding protocols and compare our methods with strategies based on bipartite entanglement purification in static and communication scenarios. We find that direct multiparty purification is of advantage with respect to achievable yields and minimal required fidelity in static scenarios, and with respect to obtainable fidelity in the case of noisy operations in both scenarios.
We investigate measurement-based entanglement purification protocols (EPP) in the presence of local noise and imperfections. We derive a universal, protocol-independent threshold for the required quality of the local resource states, where we show that local noise per particle of up to 24% is tolerable. This corresponds to an increase of the noise threshold by almost an order of magnitude, based on the joint measurement-based implementation of sequential rounds of few-particle EPP. We generalize our results to multipartite EPP, where we encounter similarly high error thresholds.
In this paper, we propose a novel bipartite entanglement purification protocol built upon hashing and upon the guessing random additive noise decoding (GRAND) approach recently devised for classical error correction codes. Our protocol offers substantial advantages over existing hashing protocols, requiring fewer qubits for purification, achieving higher fidelities, and delivering better yields with reduced computational costs. We provide numerical and semi-analytical results to corroborate our findings and provide a detailed comparison with the hashing protocol of Bennet et al. Although that pioneering work devised performance bounds, it did not offer an explicit construction for implementation. The present work fills that gap, offering both an explicit and more efficient purification method. We demonstrate that our protocol is capable of purifying states with noise on the order of 10% per Bell pair even with a small ensemble of 16 pairs. The work explores a measurement-based implementation of the protocol to address practical setups with noise. This work opens the path to practical and efficient entanglement purification using hashing-based methods with feasible computational costs. Compared to the original hashing protocol, the proposed method can achieve some desired fidelity with a number of initial resources up to one hundred times smaller. Therefore, the proposed method seems well-fit for future quantum networks with a limited number of resources and entails a relatively low computational overhead.
We introduce entanglement purification protocols for ddd-level systems (qudits) with improved efficiency as compared to previous protocols. While we focus on protocols for bipartite systems, we also propose generalizations to multipartite qudit systems. The schemes we introduce include recurrence protocols that operate on two copies, as well as hashing protocols that operate on large ensembles. We analyze properties of the protocols with respect to minimal required fidelity and yield, and study their performance in the presence of noise and imperfections. We determine error thresholds and study the dependence on local dimension. We find that our schemes do not only outperform previous approaches, but also show an improved robustness and better efficiency with increasing dimension. While error thresholds for different system sizes are not directly comparable, our results nevertheless suggest that quantum information processing using qudits, in particular for long-distance quantum communication, may offer an advantage over approaches based on qubit systems.