Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0407021 · Physical Review A

Error filtration and entanglement purification for quantum communication

Nicolas Gisin, Noah Linden, Serge Massar, Sandu Popescu

Published Jul 28, 2005• 63 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.72.012338

Related papers

Entanglement purification and quantum error correction

Wolfgang Dür, Hans J. Briegel

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.

arXiv:0705.4165•Reports on Progress in Physics•Jul 17, 2007•330 citations

Combating errors in quantum communication: an integrated approach

Rajni Bala, Sooryansh Asthana, V. Ravishankar

Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty higher dimensional entanglement is not easy. This calls for exploring realistic solutions which are implementable with current devices. Motivated particularly by the difficulty in generation of multiparty entangled states, in this paper, we have investigated error-free information transfer with minimal requirements. For this, we have proposed a new information encoding scheme for communication purposes. The encoding scheme is based on the fact that most noisy channels leave some quantities invariant. Armed with this fact, we encode information in these invariants. These invariants are functions of expectation values of operators. This information passes through the noisy channel unchanged. Pertinently, this approach is not in conflict with other existing error correction schemes. In fact, we have shown how standard quantum error-correcting codes emerge if suitable restrictions are imposed on the choices of logical basis states. As applications, for illustration, we propose a quantum key distribution protocol and an error-immune information transfer protocol.

arXiv:2208.04555•Scientific Reports•Feb 20, 2023•6 citations

Quantum Error Correction Information Encoder

Jincheng Zhang

This paper presents a novel quantum error correction information encoder designed to mitigate the detrimental effects of decoherence on quantum information. The core of the proposed scheme relies on exploiting multi-particle entanglement to establish a robust coding strategy. The system utilizes a carefully crafted sequence of measurements to detect and correct errors effectively, while simultaneously minimizing the required redundancy. The fundamental difference from existing classical error correction methods lies in the leveraging of quantum mechanical phenomena, specifically entanglement, to ensure information integrity. This approach offers a potential pathway towards reliable quantum communication and computation, addressing a critical bottleneck in the field. The theoretical framework is presented, outlining the key components and operational principles of the encoder. The presented model is scalable and adaptable, providing a foundation for future research and development in quantum error correction technologies.

•Sep 5, 2026•0 citations

Quantum Entanglement Information Encoding & Error Correction

Jincheng Zhang

This paper investigates a novel approach to information encoding and error correction leveraging the unique properties of quantum entanglement. The core claim is to construct an information encoding scheme based on entangled states, complemented by quantum error correction codes, to achieve high-efficiency information transmission and storage. The proposed mechanism utilizes multi-body quantum entanglement for encoding, exploiting the correlated nature of entangled states, alongside the development of a specialized quantum error correction code designed to specifically address errors within entangled states. The research demonstrates a potential pathway exceeding the limitations of classical encoding, offering the possibility of superluminal information transfer by directly utilizing the correlations inherent in entanglement and implementing targeted error correction. The theoretical framework presented provides a foundation for future research into scalable quantum communication and data storage systems. The key mathematical components explored include the density matrix formalism, Pauli operators, and the concepts of quantum error correction codes, specifically focusing on their application to entangled states. The primary objective is to establish a robust and efficient method for encoding and correcting information using quantum entanglement, a crucial step towards realizing practical quantum communication networks.

•Sep 7, 2026•0 citations

Quantum repeaters based on entanglement purification

Wolfgang Dür, Hans J. Briegel, J. I. Cirac +1 more

We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.

arXiv:quant-ph/9808065•Physical Review A•Jan 1, 1999•795 citations

Protecting quantum entanglement by repetitive measurement

Cornelis Christiaan Bultink

Information processing based on the laws of quantum mechanics promises to be a revolutionary new avenue in information technology. This emerging field of quantum information processing (QIP) is however challenged by the fragile nature of the quantum bits (qubits) in which quantum information is stored and processed. An error in even a single qubit makes the quantum processor go off-track, corrupting the calculation as a whole. Therefore, the chance for an erroneous outcome increases with the number of qubits in the processor. Large-scale QIP thus hinges on the ability to correct for these errors. Classical information processing often uses error correction algorithms to identify errors by checking whether information is consistent in multiple copies. This strategy is unfortunately not applicable to QIP as quantum states cannot be copied. Moreover, direct measurements on qubits collapse their quantum states, reducing them to classical information. Fortunately, the theory of quantum error correction (QEC) overcomes these complications by encoding quantum information in entangled states of many qubits and performing parity measurements to identify errors in the system without destroying the encoded information. Implementing these codes is challenging as it requires many qubits and quick interleaving of operations and measurements. Moreover, to not introduce more errors in the system than QEC can solve for, these operations and measurements need to be of sufficient fidelity and speed...

•Aug 24, 2020•1 citation
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.
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.
Near-term quantum communication protocols suffer inevitably from channel noises, whose alleviation has been mostly attempted with resources such as multiparty entanglement or sophisticated experimental techniques. Generation of multiparty higher dimensional entanglement is not easy. This calls for exploring realistic solutions which are implementable with current devices. Motivated particularly by the difficulty in generation of multiparty entangled states, in this paper, we have investigated error-free information transfer with minimal requirements. For this, we have proposed a new information encoding scheme for communication purposes. The encoding scheme is based on the fact that most noisy channels leave some quantities invariant. Armed with this fact, we encode information in these invariants. These invariants are functions of expectation values of operators. This information passes through the noisy channel unchanged. Pertinently, this approach is not in conflict with other existing error correction schemes. In fact, we have shown how standard quantum error-correcting codes emerge if suitable restrictions are imposed on the choices of logical basis states. As applications, for illustration, we propose a quantum key distribution protocol and an error-immune information transfer protocol.
This paper presents a novel quantum error correction information encoder designed to mitigate the detrimental effects of decoherence on quantum information. The core of the proposed scheme relies on exploiting multi-particle entanglement to establish a robust coding strategy. The system utilizes a carefully crafted sequence of measurements to detect and correct errors effectively, while simultaneously minimizing the required redundancy. The fundamental difference from existing classical error correction methods lies in the leveraging of quantum mechanical phenomena, specifically entanglement, to ensure information integrity. This approach offers a potential pathway towards reliable quantum communication and computation, addressing a critical bottleneck in the field. The theoretical framework is presented, outlining the key components and operational principles of the encoder. The presented model is scalable and adaptable, providing a foundation for future research and development in quantum error correction technologies.
This paper investigates a novel approach to information encoding and error correction leveraging the unique properties of quantum entanglement. The core claim is to construct an information encoding scheme based on entangled states, complemented by quantum error correction codes, to achieve high-efficiency information transmission and storage. The proposed mechanism utilizes multi-body quantum entanglement for encoding, exploiting the correlated nature of entangled states, alongside the development of a specialized quantum error correction code designed to specifically address errors within entangled states. The research demonstrates a potential pathway exceeding the limitations of classical encoding, offering the possibility of superluminal information transfer by directly utilizing the correlations inherent in entanglement and implementing targeted error correction. The theoretical framework presented provides a foundation for future research into scalable quantum communication and data storage systems. The key mathematical components explored include the density matrix formalism, Pauli operators, and the concepts of quantum error correction codes, specifically focusing on their application to entangled states. The primary objective is to establish a robust and efficient method for encoding and correcting information using quantum entanglement, a crucial step towards realizing practical quantum communication networks.
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is possible, however, to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An important question is how the noise, introduced by imperfect local operations (that constitute the protocols of purification and the entanglement swapping), accumulates in such a compound channel, and how it can be kept below a certain noise level. To treat this problem, we first study the applicability and the efficiency of entanglement purification protocols in the situation of imperfect local operations. We then present a scheme that allows entanglement purification over arbitrary long channels and tolerates errors on the percent level. It requires a polynomial overhead in time, and an overhead in local resources that grows only logarithmically with the length of the channel.
Information processing based on the laws of quantum mechanics promises to be a revolutionary new avenue in information technology. This emerging field of quantum information processing (QIP) is however challenged by the fragile nature of the quantum bits (qubits) in which quantum information is stored and processed. An error in even a single qubit makes the quantum processor go off-track, corrupting the calculation as a whole. Therefore, the chance for an erroneous outcome increases with the number of qubits in the processor. Large-scale QIP thus hinges on the ability to correct for these errors. Classical information processing often uses error correction algorithms to identify errors by checking whether information is consistent in multiple copies. This strategy is unfortunately not applicable to QIP as quantum states cannot be copied. Moreover, direct measurements on qubits collapse their quantum states, reducing them to classical information. Fortunately, the theory of quantum error correction (QEC) overcomes these complications by encoding quantum information in entangled states of many qubits and performing parity measurements to identify errors in the system without destroying the encoded information. Implementing these codes is challenging as it requires many qubits and quick interleaving of operations and measurements. Moreover, to not introduce more errors in the system than QEC can solve for, these operations and measurements need to be of sufficient fidelity and speed...