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Quantum Science and Technology

High dimensional quantum network coding based on prediction mechanism over the butterfly network

Xing-Bo Pan, Xiu‐Bo Chen, Gang Xu, Zongpeng Li, Yixian Yang

Published Oct 26, 2021• 9 citations
Publisher

Abstract

Abstract The high-dimensional quantum system greatly improve the quantum channel capacity and information storage space, and achieve high-dimensional quantum information transmission, which enhance the speed of quantum computing and quantum information processing. In this paper, a high-dimensional quantum teleportation protocol without information loss is proposed. We consider pre-sharing a high-dimensional non-maximum entangled state as a quantum channel between sender and receiver. By adding auxiliary particle and performing high-dimensional local operations, it is possible to achieve high-dimensional quantum teleportation without information loss. Simultaneously, we apply the protocol to butterfly network, and propose a novel high-dimensional quantum network coding based on prediction mechanism. In our scheme, we use Z -{|0⟩, |1⟩} basis to predict the transmission of high dimensional states over the butterfly network. When the prediction is successful, the deterministic transmission of high-dimensional quantum states can be realized over the butterfly network. Our scheme greatly saves the usage of quantum and classical channels, which improves the utilization efficiency of both channels.

DOI
10.1088/2058-9565/ac3387

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Abstract The high-dimensional quantum system greatly improve the quantum channel capacity and information storage space, and achieve high-dimensional quantum information transmission, which enhance the speed of quantum computing and quantum information processing. In this paper, a high-dimensional quantum teleportation protocol without information loss is proposed. We consider pre-sharing a high-dimensional non-maximum entangled state as a quantum channel between sender and receiver. By adding auxiliary particle and performing high-dimensional local operations, it is possible to achieve high-dimensional quantum teleportation without information loss. Simultaneously, we apply the protocol to butterfly network, and propose a novel high-dimensional quantum network coding based on prediction mechanism. In our scheme, we use Z -{|0⟩, |1⟩} basis to predict the transmission of high dimensional states over the butterfly network. When the prediction is successful, the deterministic transmission of high-dimensional quantum states can be realized over the butterfly network. Our scheme greatly saves the usage of quantum and classical channels, which improves the utilization efficiency of both channels.
Quantum secret-sharing is a fundamental technique in quantum communication and plays a crucial role in high-dimensional quantum secret transmission. This paper investigates the teleportation of arbitrary d-dimensional multipartite quantum secrets and proposes both deterministic and probabilistic teleportation protocols. The schemes employ generalized Bell-state measurements, generalized Pauli operators, and auxiliary particles to achieve efficient and secure quantum secret-sharing. The deterministic protocol employs maximally entangled channels to achieve perfect sharing with unit success probability. Moreover, the probabilistic protocol, assisted by auxiliary particles and generalized unitary operations, achieves perfect fidelity quantum secret sharing via non-maximally entangled channels. The protocols are further extended to arbitrary d-dimensional systems, and their robustness under several common quantum noise models is analyzed numerically. Compared with previous schemes, the proposed protocols support arbitrary multipartite entangled states, high-dimensional systems, non-maximally entangled channels, and noise analysis within a unified framework. These results enrich the theory of high-dimensional quantum communication and provide practical approaches for future quantum secret-sharing and secure quantum networks.
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.
Inspired by the structure of the network coding over the butterfly network, a framework of quantum network coding scheme is investigated, which transmits two unknown quantum states crossly over the butterfly quantum system with the multi-photon non-maximally entangled GHZ states. In this scheme, it contains certain number of entanglement-qubit source nodes that teleport unknown quantum states to other nodes on the small-scale network where each intermediate node can pass on its received quantum states to others via superdense coding. In order to transmit the unknown states in a deterministic way, the controlled quantum teleportation is adopted on the intermediate node. It makes legal nodes more convenient than any other previous teleportation schemes to transmit unknown quantum states to unknown participants in applications. It shows that the intrinsic efficiency of transmissions approaches 100% in principle. This scheme is secure based on the securely-shared quantum channels between all nodes and the quantum mechanical impossibility of local unitary transformations between non-maximally entangled GHZ states. Moreover, the generalized scheme is proposed for transmitting two multipartite entangled states. DOI:  http://dx.doi.org/10.11591/telkomnika.v11i2.2031
the purpose of this paper is to promote a butterfly quantum network coding scheme for remote state preparation of multi-qudit states. Firstly, we perform channel preparation and amplitude modulation; secondly, each sender simultaneously performs projection measurement; thirdly, both senders send measurement results as precoding information and auxiliary information to the intermediate node and the neighboring receivers respectively; fourthly, the first intermediate node performs encoding operation and sends the encoded information to both receivers via next intermediate node. Finally, by decoding the coded information with auxiliary information, two receivers perform corresponding unitary operations to recover the target multi-qudit quantum states. Compared with other schemes, our scheme can enhance the throughput and transmission efficiency of communication network for remote state preparation of multi-qudit states.
Abstract We present an innovative approach for quantum teleportation (QT) in a three-dimensional (3D) quantum system, enabling the transmission of 3D quantum information from multiple senders to multiple receivers using a 3D maximally entangled GHZ-type state as a network channel.By substituting the quantum channel with a partially entangled GHZ-type state in a three-dimensional (3D) setting, we obtain an extension of the above scheme in which, when an auxiliary qubit is introduced, the receivers implement a two-particle unitary transformation and some proper 3D Weyl operators to jointly reconstruct the transmitted state with a certain probability and unit fidelity. Subsequently, inspired by the proposed schemes, a protocol for transferring a shared d-dimensional (dD) quantum state to multiple distant parties by using a dD maximally entangled GHZ-type state as quantum channel is presented, and it is generalized to the case of a dD partially entangled GHZ-type network channel by introducing an auxiliary qubit and executing a two-particle unitary transformation. Our schemes can relay quantum information over a network without requiring fully trusted central or intermediate nodes, and none of the participants can fully accesses the information.
Abstract Distributing quantum state and entanglement between distant nodes is a crucial task in distributed quantum information processing on large-scale quantum networks. Quantum network coding provides an alternative solution for quantum-state distribution, especially when the bottleneck problems must be considered and high communication speed is required. Here, we report the first experimental realization of quantum network coding on the butterfly network. With the help of prior entanglements shared between senders, two quantum states can be transmitted perfectly through the butterfly network. We demonstrate this protocol by employing eight photons generated via spontaneous parametric downconversion. We observe cross-transmission of single-photon states with an average fidelity of 0.9685 ± 0.0013, and that of two-photon entanglement with an average fidelity of 0.9611 ± 0.0061, both of which are greater than the theoretical upper bounds without prior entanglement.