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.
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.
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 qr-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.
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.
This paper considers the communication over a quantum multiple-unicast network where r sender-receiver pairs communicate independent quantum states. We concretely construct a quantum network code for the quantum multiple-unicast network as a generalization of the code [Song and Hayashi, arxiv:1801.03306, 2018] for the quantum unicast network. When the given node operations are restricted to invertible linear operations between bit basis states and the rates of transmissions and interferences are restricted, our code certainly transmits a quantum state for each sender-receiver pair by n-use of the network asymptotically, which guarantees no information leakage to the other users. Our code is implemented only by the coding operation in the senders and receivers and employs no classical communication and no manipulation of the node operations. Several networks that our code can be applied are also given.
Classical network coding uses encoding of information over networks to achieve secure and high throughput communication with low latency. Its quantum analog, namely Quantum Network Coding (QNC) is a promising protocol to achieve quantum communication over quantum networks. In this paper, we propose a method for establishing QNC in Measurement-Based Quantum Computing (MBQC), which is a universal quantum computational model. We demonstrate that the problem of multiple unicast or multiple multicast of distinct computational basis states over a quantum network can be solved by simulating existing classical networks, with the CNOT implementation in MBQC as a basis for transmitting and encoding of states. We also show how it can be further extended to simultaneously distribute the Bell pairs and Greenberger–Horne–Zeilinger (GHZ) states required for quantum communication between distant transmitter and corresponding receiver nodes of a network.
Abstract We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network. In this paper, we propose the quantum 2-pair multicast communication scheme, and extend it to k-pair multicast communication over the extended butterfly network. Firstly, an EPR pair is shared between each adjacent node on the butterfly network, and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes. Secondly, each sender adds auxiliary particles according to the multicast number k, in which the CNOT operations are applied to form the multi-particle entangled state. Finally, combined with network coding and free classical communication, quantum multicast communication based on quantum measurements is completed over the extended butterfly network. Not only the bottleneck problem is solved, but also quantum multicast communication can be completed in our scheme. At the same time, regardless of multicast number k, the maximum capacity of classical channel is 2 bits, and quantum channel is used only once.