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:1908.00705 · Applied Sciences

Asymmetric Quantum Multicast Network Coding: Asymmetric Optimal Cloning over Quantum Networks

Yuichi Hirota, Masaki Owari

Published Jun 17, 2022• 7 citations
arXivHTMLPDF

Abstract

Multicasting of quantum states is an essential feature of quantum internet. Since the noncloning theorem prohibits perfect cloning of an unknown quantum state, an appropriate protocol may depend on the purpose of the multicast. In this paper, we treat the multicasting of a single copy of an unknown state over a quantum network with free classical communication. We especially focus on protocols exactly multicasting an asymmetric optimal universal clone. Hence, these protocols are optimal and universal in terms of mean fidelity between input and output states, but the fidelities can depend on target nodes. Among these protocols, a protocol spending smaller communication resources is preferable. Here, we construct such a protocol attaining the min-cut of the network described as follows. Two (three) asymmetric optimal clones of an input state are created at a source node. Then, the state is divided into classical information and a compressed quantum state. The state is sent to two (three) target nodes using the quantum network coding. Finally, the asymmetric clones are reconstructed using LOCC with a small amount of entanglement shared among the target nodes and the classical information sent from the source node.

DOI
10.3390/app12126163

Related papers

Multicast quantum network coding as optimal symmetric universal cloning over a quantum network

Go Kato, Mio Murao, Masaki Owari

We study the problem of perfectly multicasting symmetric universal clones of unknown quantum states over quantum networks with free classical communication. We construct a protocol that multicasts symmetric universal clones of input states from multiple source nodes by extending the quantum network coding protocol proposed by Kobayashi et al. We further establish a sufficient condition for perfect multicast in the single-source setting. Specifically, we show that when a single copy of a $q^r$-dimensional input state is available at the source node, where $q$ is a sufficiently large prime power, perfect multicast of the corresponding symmetric universal clone is achievable using a small amount of entanglement shared among the target nodes. This result holds for quantum networks represented by an undirected graph $G$, where each edge corresponds to a noiseless $q$-dimensional quantum channel, provided that there exists an acyclic directed graph $G'$ obtained by assigning directions to the edges of $G$ such that the minimum cut of $G'$ is at least $r$.

quant-pharXiv:2608.18471•Lecture notes in electrical engineering•Aug 20, 2026•0 citations

Quantum network coding with adjustable fidelity

Yuchen Liu, Tao Shang, Jiayu Liu

Multicast of unknown quantum states is an unavoidable issue in the construction of quantum networks. Most existing quantum network coding schemes can only restore an unknown state at one of the target nodes during multicast. In this paper, we propose a quantum network coding scheme to multicast unknown quantum states in networks with linear network coding. Concretely, GHZ states are generated between each sender and all receivers. Unknown states are then sent and stored in the entangled state shared by the receivers. Finally, the receivers use asymmetric optimal universal cloning to obtain the required states. The scheme achieved to multicast within 1 quantum transmission and 2 classical transmissions in networks with constrained classical communication. Compared to other schemes, our scheme allows receivers to autonomously adjust the fidelity without the sender knowing the requirements.

Quantum Review Letters•Jan 1, 2025•2 citations

Perfect quantum network communication protocol based on classical network coding

Hirotada Kobayashi, François Le Gall, Harumichi Nishimura +1 more

This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that classical communication is free. The task is to perfectly transfer an unknown quantum state from a source subsystem to a target subsystem, where both source and target are formed by ordered sets of some of the nodes. It is proved that a lower bound of the rate at which this quantum communication task is possible is given by the classical min-cut max-flow theorem of network coding, where the capacities in question are the quantum capacities of the edges of the network.

arXiv:0902.1299•IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2010•79 citations

A Multicast Scheme Based on Fidelity Metrics in Quantum Networks

Xiaojun Wang, Long-Xi An, Fan‐Xu Meng +2 more

A multicast scheme based on fidelity metrics in quantum networks is proposed in this paper. First of all, according to the fidelity of copies in an asymmetric mechanism of 1→ 1+ 1+ 1+1 which is derived, the way of information transmission in the quantum networks is defined: one is one-to-one transmission based on the teleportation and the other is one-to-many lossy transmission based on quantum cloning mechanism. Second, in a specified quantum network which is a connected graph, a source node can randomly assign multicast group members. Then, with constraints of the number of replicas and the maximum number of hops of the shortest path, an optimal multicast tree is constructed to obtain maximum fidelity. Finally, the simulation results show that the proposed scheme can select the optimal path from the source node to the multicast members for the specified quantum network. With the increase of multicast group members, the average value of information fidelity obtained by all members decreases. Compared with the multicast tree constructed by the KMB algorithm, which is used to construct the Steiner tree in classical communication, the proposed schemes make the information fidelity obtained by multicast group members improve significantly.

IEEE Access•Jan 1, 2019•6 citations

Experimental realization of 1→2 asymmetric phase-covariant quantum cloning

Hongwei Chen, Xianyi Zhou, Dieter Suter +1 more

While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case of asymmetric cloning, the information from the input state is distributed asymmetrically between the different output states. Here, we consider asymmetric phase-covariant cloning, where the goal is to optimally transfer the phase information from a single input qubit to different output qubits. We construct an optimal quantum cloning machine for two qubits that does not require ancilla qubits and implement it on an NMR quantum information processor.

arXiv:quant-ph/0612132•Physical Review A•Jan 17, 2007•69 citations

Quantum Network Coding for General Graphs

Kazuo Iwama, Harumichi Nishimura, Rudy Raymond +1 more

Network coding is often explained by using a small network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which share a single bottleneck channel of capacity one. So, if we consider conventional flow (of liquid, for instance), then the total amount of flow must be at most one in total, say 1/2 for each path. However, if we consider information flow, then we can send two bits (one for each path) at the same time by exploiting two side links, which are of no use for the liquid-type flow, and encoding/decoding operations at each node. This is known as network coding and has been quite popular since its introduction by Ahlswede, Cai, Li and Yeung in 2000. In QIP 2006, Hayashi et al showed that quantum network coding is possible for Butterfly, namely we can send two qubits simultaneously with keeping their fidelity strictly greater than 1/2. In this paper, we show that the result can be extended to a large class of general graphs by using a completely different approach. The underlying technique is a new cloning method called entanglement-free cloning which does not produce any entanglement at all. This seems interesting on its own and to show its possibility is an even more important purpose of this paper. Combining this new cloning with approximation of general quantum states by a small number of fixed ones, we can design a quantum network coding protocol which ``simulates'' its classical counterpart for the same graph.

arXiv:quant-ph/0611039•Nov 3, 2006•17 citations
Multicasting of quantum states is an essential feature of quantum internet. Since the noncloning theorem prohibits perfect cloning of an unknown quantum state, an appropriate protocol may depend on the purpose of the multicast. In this paper, we treat the multicasting of a single copy of an unknown state over a quantum network with free classical communication. We especially focus on protocols exactly multicasting an asymmetric optimal universal clone. Hence, these protocols are optimal and universal in terms of mean fidelity between input and output states, but the fidelities can depend on target nodes. Among these protocols, a protocol spending smaller communication resources is preferable. Here, we construct such a protocol attaining the min-cut of the network described as follows. Two (three) asymmetric optimal clones of an input state are created at a source node. Then, the state is divided into classical information and a compressed quantum state. The state is sent to two (three) target nodes using the quantum network coding. Finally, the asymmetric clones are reconstructed using LOCC with a small amount of entanglement shared among the target nodes and the classical information sent from the source node.
We study the problem of perfectly multicasting symmetric universal clones of unknown quantum states over quantum networks with free classical communication. We construct a protocol that multicasts symmetric universal clones of input states from multiple source nodes by extending the quantum network coding protocol proposed by Kobayashi et al. We further establish a sufficient condition for perfect multicast in the single-source setting. Specifically, we show that when a single copy of a qrq^rqr-dimensional input state is available at the source node, where qqq is a sufficiently large prime power, perfect multicast of the corresponding symmetric universal clone is achievable using a small amount of entanglement shared among the target nodes. This result holds for quantum networks represented by an undirected graph GGG, where each edge corresponds to a noiseless qqq-dimensional quantum channel, provided that there exists an acyclic directed graph G′G'G′ obtained by assigning directions to the edges of GGG such that the minimum cut of G′G'G′ is at least rrr.
Multicast of unknown quantum states is an unavoidable issue in the construction of quantum networks. Most existing quantum network coding schemes can only restore an unknown state at one of the target nodes during multicast. In this paper, we propose a quantum network coding scheme to multicast unknown quantum states in networks with linear network coding. Concretely, GHZ states are generated between each sender and all receivers. Unknown states are then sent and stored in the entangled state shared by the receivers. Finally, the receivers use asymmetric optimal universal cloning to obtain the required states. The scheme achieved to multicast within 1 quantum transmission and 2 classical transmissions in networks with constrained classical communication. Compared to other schemes, our scheme allows receivers to autonomously adjust the fidelity without the sender knowing the requirements.
This paper considers a problem of quantum communication between parties that are connected through a network of quantum channels. The model in this paper assumes that there is no prior entanglement shared among any of the parties, but that classical communication is free. The task is to perfectly transfer an unknown quantum state from a source subsystem to a target subsystem, where both source and target are formed by ordered sets of some of the nodes. It is proved that a lower bound of the rate at which this quantum communication task is possible is given by the classical min-cut max-flow theorem of network coding, where the capacities in question are the quantum capacities of the edges of the network.
A multicast scheme based on fidelity metrics in quantum networks is proposed in this paper. First of all, according to the fidelity of copies in an asymmetric mechanism of 1→ 1+ 1+ 1+1 which is derived, the way of information transmission in the quantum networks is defined: one is one-to-one transmission based on the teleportation and the other is one-to-many lossy transmission based on quantum cloning mechanism. Second, in a specified quantum network which is a connected graph, a source node can randomly assign multicast group members. Then, with constraints of the number of replicas and the maximum number of hops of the shortest path, an optimal multicast tree is constructed to obtain maximum fidelity. Finally, the simulation results show that the proposed scheme can select the optimal path from the source node to the multicast members for the specified quantum network. With the increase of multicast group members, the average value of information fidelity obtained by all members decreases. Compared with the multicast tree constructed by the KMB algorithm, which is used to construct the Steiner tree in classical communication, the proposed schemes make the information fidelity obtained by multicast group members improve significantly.
While exact cloning of an unknown quantum state is prohibited by the linearity of quantum mechanics, approximate cloning is possible and has been used, e.g., to derive limits on the security of quantum communication protocols. In the case of asymmetric cloning, the information from the input state is distributed asymmetrically between the different output states. Here, we consider asymmetric phase-covariant cloning, where the goal is to optimally transfer the phase information from a single input qubit to different output qubits. We construct an optimal quantum cloning machine for two qubits that does not require ancilla qubits and implement it on an NMR quantum information processor.
Network coding is often explained by using a small network model called Butterfly. In this network, there are two flow paths, s_1 to t_1 and s_2 to t_2, which share a single bottleneck channel of capacity one. So, if we consider conventional flow (of liquid, for instance), then the total amount of flow must be at most one in total, say 1/2 for each path. However, if we consider information flow, then we can send two bits (one for each path) at the same time by exploiting two side links, which are of no use for the liquid-type flow, and encoding/decoding operations at each node. This is known as network coding and has been quite popular since its introduction by Ahlswede, Cai, Li and Yeung in 2000. In QIP 2006, Hayashi et al showed that quantum network coding is possible for Butterfly, namely we can send two qubits simultaneously with keeping their fidelity strictly greater than 1/2. In this paper, we show that the result can be extended to a large class of general graphs by using a completely different approach. The underlying technique is a new cloning method called entanglement-free cloning which does not produce any entanglement at all. This seems interesting on its own and to show its possibility is an even more important purpose of this paper. Combining this new cloning with approximation of general quantum states by a small number of fixed ones, we can design a quantum network coding protocol which ``simulates'' its classical counterpart for the same graph.