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

Long distance quantum communication over noisy networks

Andrzej Grudka, Ëukasz Pankowski

Published Feb 5, 2012• 1 citation
OpenAlex

Abstract

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long distance entanglement sharing and communication exploits networks, whose nodes share EPR pairs. In [Perseguers et al., Phys. Rev. A 78,062324 (2008)] an important isomorphism between storing quantum information in dimension D and transmission of quantum information in D + 1 network has been put forward. It implies that fault tolerant quantum computing allows in principle for long distance quantum communication. However, in fault-tolerant schemes, one usually considers creating known encoded states. However the process of encoding and decoding is exposed to error. We show that during this stage fidelity drops by a constant factor related to the volume of circuit that replaces a gate, while going to an upper level of concatenation. This shows explicitly, that it is possible to obtain long distance entanglement in 2D network. For 3D networks, much simpler schemes are possible, e.g. due to existence of Kitaev topological quantum memory, shich uses 2D lattice. Again, we consider explicitly the encoding and decoding stages. In [Dennis et al. J. Math. Phys. 43, 4452 (2002)] such scheme was provided in terms of gates. Here we propose a very simple scheme, based solely on syndrome measurements. It is then showed that the scheme is equivalent to teleporting the state to be encoded through some virtual EPR pair existing within the rest of qubits. We then present numerical simulation of performance of such encoding/decoding scheme.

Related papers

Long-distance quantum communication over noisy networks without long-time quantum memory

Paweł Mazurek, Andrzej Grudka, Michał Horodecki +4 more

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension $D$ and transmission of quantum information in a $D+1$-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.

arXiv:1202.1016•Physical Review A•Dec 4, 2014•23 citations

One-shot entanglement generation over long distances in noisy quantum networks

Sébastien Perseguers, Liang Jiang, Norbert Schuch +4 more

We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the effective probability for the quantum errors is below a certain threshold, which is achieved by a local encoding of the qubits and a global bit-flip correction. In contrast to the conventional quantum-repeater schemes, we do not need to store the qubits in quantum memory for a long time: our protocol is a one-shot process (i.e., the elementary entangled pairs are used only once) involving one-way classical communication. Furthermore, the overhead of local resources increases only logarithmically with the size of the network, making our proposal favorable to long-distance quantum communication.

arXiv:0807.0208•Physical Review A•Dec 12, 2008•33 citations

Fault-tolerant and secure long-distance quantum communication via uncorrectable-error-injection

IlKwon Sohn, B.H. Kim, Kwangil Bae +4 more

Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification, leading to significant resource overhead and operational complexity. In this study, we propose a novel fault-tolerant and secure quantum communication scheme based on uncorrectable error injection. Our method exploits a quantum state encoding scheme based on quantum error correction codes, which strategically introduces uncorrectable errors to enhance security. It eliminates the need for entanglement distribution while reducing resource requirements. The injected errors protect against eavesdropping by preventing unauthorized parties from retrieving meaningful information. Security analysis shows that as the data length and encoded message size increase, information leakage becomes negligible relative to the size of the total message. Comparative performance analysis with existing approaches indicates that our method reduces transmission overhead while maintaining comparable fidelity in low-error regimes. These findings suggest that the proposed method offers a scalable and practical alternative for secure long-distance quantum communication, distributed quantum computing, and future quantum internet applications.

arXiv:2411.14710•EPJ Quantum Technology•Nov 11, 2025•1 citation

Shortcuts to quantum network routing

Eddie Schoute, Laura Mančinska, Tanvirul Islam +2 more

A quantum network promises to enable long distance quantum communication, and assemble small quantum devices into a large quantum computing cluster. Each network node can thereby be seen as a small few qubit quantum computer. Qubits can be sent over direct physical links connecting nearby quantum nodes, or by means of teleportation over pre-established entanglement amongst distant network nodes. Such pre-shared entanglement effectively forms a shortcut - a virtual quantum link - which can be used exactly once. Here, we present an abstraction of a quantum network that allows ideas from computer science to be applied to the problem of routing qubits, and manage entanglement in the network. Specifically, we consider a scenario in which each quantum network node can create EPR pairs with its immediate neighbours over a physical connection, and perform entanglement swapping operations in order to create long distance virtual quantum links. We proceed to discuss the features unique to quantum networks, which call for the development of new routing techniques. As an example, we present two simple hierarchical routing schemes for a quantum network of N nodes for a ring and sphere topology. For these topologies we present efficient routing algorithms requiring O(log N) qubits to be stored at each network node, O(polylog N) time and space to perform routing decisions, and O(log N) timesteps to replenish the virtual quantum links in a model of entanglement generation.

arXiv:1610.05238•Oct 17, 2016•95 citations

Entanglement Distribution in Quantum Networks

Sébastien Perseguers

This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular.We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings.The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement.First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links).We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem.We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement.Second, we consider a mixed-state definition of the connections of the quantum networks.This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs.New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations.Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance.Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a few links only.Based on the theory of random graphs, we propose a model of quantum complex networks, which exhibit some totally unexpected properties compared to their classical counterparts.5.1 Propagation of a large GHZ state through the lattice . . .5.2 Bit-flip error correction . . . . . . . . . . . . .

•Jan 1, 2010•6 citations

Fault-Tolerant Coding for Quantum Communication

Matthias Christandl, Alexander Müller‐Hermes

Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. We introduce fault-tolerant versions of quantum capacities quantifying the optimal communication rates achievable with asymptotically vanishing total error when the encoding and decoding circuits are affected by gate errors with small probability. Our main results are threshold theorems for the classical and quantum capacity: For every quantum channel$T$and every$\epsilon >0$there exists a threshold$p(\epsilon,T)$for the gate error probability below which rates larger than$C-\epsilon $are fault-tolerantly achievable with vanishing overall communication error, where$C$denotes the usual capacity. Our results are not only relevant in communication over large distances, but also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise than affecting the local gates.

arXiv:2009.07161•IEEE Transactions on Information Theory•Apr 21, 2022•15 citations
The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long distance entanglement sharing and communication exploits networks, whose nodes share EPR pairs. In [Perseguers et al., Phys. Rev. A 78,062324 (2008)] an important isomorphism between storing quantum information in dimension D and transmission of quantum information in D + 1 network has been put forward. It implies that fault tolerant quantum computing allows in principle for long distance quantum communication. However, in fault-tolerant schemes, one usually considers creating known encoded states. However the process of encoding and decoding is exposed to error. We show that during this stage fidelity drops by a constant factor related to the volume of circuit that replaces a gate, while going to an upper level of concatenation. This shows explicitly, that it is possible to obtain long distance entanglement in 2D network. For 3D networks, much simpler schemes are possible, e.g. due to existence of Kitaev topological quantum memory, shich uses 2D lattice. Again, we consider explicitly the encoding and decoding stages. In [Dennis et al. J. Math. Phys. 43, 4452 (2002)] such scheme was provided in terms of gates. Here we propose a very simple scheme, based solely on syndrome measurements. It is then showed that the scheme is equivalent to teleporting the state to be encoded through some virtual EPR pair existing within the rest of qubits. We then present numerical simulation of performance of such encoding/decoding scheme.
The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008)] the authors put forward an important isomorphism between storing quantum information in a dimension DDD and transmission of quantum information in a D+1D+1D+1-dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.
We consider the problem of creating a long-distance entangled state between two stations of a network, where neighboring nodes are connected by noisy quantum channels. We show that any two stations can share an entangled pair if the effective probability for the quantum errors is below a certain threshold, which is achieved by a local encoding of the qubits and a global bit-flip correction. In contrast to the conventional quantum-repeater schemes, we do not need to store the qubits in quantum memory for a long time: our protocol is a one-shot process (i.e., the elementary entangled pairs are used only once) involving one-way classical communication. Furthermore, the overhead of local resources increases only logarithmically with the size of the network, making our proposal favorable to long-distance quantum communication.
Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification, leading to significant resource overhead and operational complexity. In this study, we propose a novel fault-tolerant and secure quantum communication scheme based on uncorrectable error injection. Our method exploits a quantum state encoding scheme based on quantum error correction codes, which strategically introduces uncorrectable errors to enhance security. It eliminates the need for entanglement distribution while reducing resource requirements. The injected errors protect against eavesdropping by preventing unauthorized parties from retrieving meaningful information. Security analysis shows that as the data length and encoded message size increase, information leakage becomes negligible relative to the size of the total message. Comparative performance analysis with existing approaches indicates that our method reduces transmission overhead while maintaining comparable fidelity in low-error regimes. These findings suggest that the proposed method offers a scalable and practical alternative for secure long-distance quantum communication, distributed quantum computing, and future quantum internet applications.
A quantum network promises to enable long distance quantum communication, and assemble small quantum devices into a large quantum computing cluster. Each network node can thereby be seen as a small few qubit quantum computer. Qubits can be sent over direct physical links connecting nearby quantum nodes, or by means of teleportation over pre-established entanglement amongst distant network nodes. Such pre-shared entanglement effectively forms a shortcut - a virtual quantum link - which can be used exactly once. Here, we present an abstraction of a quantum network that allows ideas from computer science to be applied to the problem of routing qubits, and manage entanglement in the network. Specifically, we consider a scenario in which each quantum network node can create EPR pairs with its immediate neighbours over a physical connection, and perform entanglement swapping operations in order to create long distance virtual quantum links. We proceed to discuss the features unique to quantum networks, which call for the development of new routing techniques. As an example, we present two simple hierarchical routing schemes for a quantum network of N nodes for a ring and sphere topology. For these topologies we present efficient routing algorithms requiring O(log N) qubits to be stored at each network node, O(polylog N) time and space to perform routing decisions, and O(log N) timesteps to replenish the virtual quantum links in a model of entanglement generation.
This Thesis contributes to the theory of entanglement distribution in quantum networks, analyzing the generation of long-distance entanglement in particular.We consider that neighboring stations share one partially entangled pair of qubits, which emphasizes the difficulty of creating remote entanglement in realistic settings.The task is then to design local quantum operations at the stations, such that the entanglement present in the links of the whole network gets concentrated between few parties only, regardless of their spatial arrangement.First, we study quantum networks with a two-dimensional lattice structure, where quantum connections between the stations (nodes) are described by non-maximally entangled pure states (links).We show that the generation of a perfectly entangled pair of qubits over an arbitrarily long distance is possible if the initial entanglement of the links is larger than a threshold.This critical value highly depends on the geometry of the lattice, in particular on the connectivity of the nodes, and is related to a classical percolation problem.We then develop a genuine quantum strategy based on multipartite entanglement, improving both the threshold and the success probability of the generation of long-distance entanglement.Second, we consider a mixed-state definition of the connections of the quantum networks.This formalism is well-adapted for a more realistic description of systems in which noise (random errors) inevitably occurs.New techniques are required to create remote entanglement in this setting, and we show how to locally extract and globally process some error syndromes in order to create useful long-distance quantum correlations.Finally, we turn to networks that have a complex topology, which is the case for most real-world communication networks such as the Internet for instance.Besides many other characteristics, these systems have in common the small-world feature, stating that any two nodes are separated by a few links only.Based on the theory of random graphs, we propose a model of quantum complex networks, which exhibit some totally unexpected properties compared to their classical counterparts.5.1 Propagation of a large GHZ state through the lattice . . .5.2 Bit-flip error correction . . . . . . . . . . . . .
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. We introduce fault-tolerant versions of quantum capacities quantifying the optimal communication rates achievable with asymptotically vanishing total error when the encoding and decoding circuits are affected by gate errors with small probability. Our main results are threshold theorems for the classical and quantum capacity: For every quantum channelTTTand everyϵ>0\epsilon >0ϵ>0there exists a thresholdp(ϵ,T)p(\epsilon,T)p(ϵ,T)for the gate error probability below which rates larger than$C-\epsilon arefault−tolerantlyachievablewithvanishingoverallcommunicationerror,whereare fault-tolerantly achievable with vanishing overall communication error, wherearefault−tolerantlyachievablewithvanishingoverallcommunicationerror,whereC$denotes the usual capacity. Our results are not only relevant in communication over large distances, but also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise than affecting the local gates.