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arXiv:0705.4165 · Reports on Progress in Physics

Entanglement purification and quantum error correction

Wolfgang Dür, Hans J. Briegel

Published Jul 17, 2007• 330 citations
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Abstract

We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on the theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing.

DOI
10.1088/0034-4885/70/8/r03

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We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on the theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied. Several applications of entanglement purification in quantum communication and computation are presented, which highlights the fact that entanglement purification is a fundamental tool in quantum information processing.
The key realization that led to the emergence of the new field of quantum information processing is that quantum mechanics, the theory that describes microscopic particles, allows the processing of information in fundamentally new ways. But just as in classical information processing, errors occur in quantum information processing, and these have to be corrected. A fundamental breakthrough was the realization that quantum error correction is in fact possible. However, most work so far has not been concerned with technological feasibility, but rather with proving that quantum error correction is possible in principle. Here we describe a method for filtering out errors and entanglement purification which is particularly suitable for quantum communication. Our method is conceptually new, and, crucially, it is easy to implement in a wide variety of physical systems with present-day technology and should therefore be of wide applicability.
Entanglement purification protocols, designed to improve the fidelity of Bell states over quantum networks for inter-node communications, have attracted significant attention over the last few decades. These protocols have great potential to resolve a core challenge in quantum networking of generating high-fidelity Bell states. However, previous studies focused on the theoretical discussion with limited consideration of realistic errors. Studies of dynamically selecting the right purification protocol under various realistic errors that occur in practice have yet to be performed. In this work, we study the performance of various purification protocols under realistic errors by conducting density matrix simulations over a large suite of error models. Based on our findings of how specific error channels affect the performance of purification protocols, we propose a module that can be embedded in the quantum network. This module determines and selects the appropriate purification protocol, considering not only expected specifications from the network layer but also the capabilities of the physical layer. Finally, the performance of our proposed module is verified using two benchmark categories. Compared with the default approach and exhaustive search approach, we show a success rate approaching 90% in identifying the optimal purification protocol for our target applications.
In this thesis, we investigate how protocols in quantum communication theory are influenced by noise. Specifically, we take into account noise during the transmission of quantum information and noise during the processing of quantum information. We describe three novel quantum communication protocols which can be accomplished efficiently in a noisy environment: (1) Factorization of Eve: We show that it is possible to disentangle transmitted qubits a posteriori from the quantum channel's degrees of freedom. (2) Cluster state purification: We give multi-partite entanglement purification protocols for a large class of entangled quantum states. (3) Entanglement purification protocols from quantum codes: We describe a constructive method to create bipartite entanglement purification protocols form quantum error correcting codes, and investigate the properties of these protocols, which can be operated in two different modes, which are related to quantum communication and quantum computation protocols, respectively.
Entanglement purification protocols are fundamental primitives in quantum communication, enabling the distillation of high-quality entanglement using only local operations and classical communication. For large multipartite states, however, existing purification schemes typically require substantial resources and become progressively inefficient as system size increases. We introduce a new type of multipartite entanglement purification, Localized Entanglement Purification (LEP), a family of protocols that purify entanglement at the level of network regions rather than globally. By exploiting spatial noise asymmetries, LEP reduces resource consumption and enables scalable purification strategies for larger quantum systems.
Abstract Quantum entanglement is a fundamental resource for quantum computing, quantum communication, and quantum cryptography. In realistic quantum channels, however, entanglement is highly susceptible to noise and decoherence. Entanglement purification(EP) and quantum error correction (QEC) offer distinct approaches to protecting entanglement against noisy quantum channels. In this work, we propose a hybrid scheme that integrates these two approaches to enhance the protection of entanglement between logical qubits. The scheme exploits both the error-correcting capability of encoded logical qubits and the distillation power of entanglement purification, assuming recovery to the logical codespace after each QEC cycle. This combined approach enables improved entanglement preservation under noisy conditions. The resulting robust logical entanglement is well-suited for applications in quantum communication and quantum cryptography and offers a promising route toward more reliable distributed quantum information processing.