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Physica Scripta

Multicast-based fault-tolerant multiparty state preparation of four-qubit cluster states

Tiantian Meng, Yuzhen Wei, Min Jiang, Hong Chen, Xu Huang

Published Aug 29, 2024• 1 citation
Publisher

Abstract

Abstract The primary aim of this study is to utilize multicast in the preparation of multi-party four-qubit cluster states. In the presence of environment noises, errors may influence the procedure of the particle distribution. To address this challenge, we propose a fault-tolerant scheme to manage the errors within the detectable channel particles. Based on the Bell chain channel, our approach could prepare arbitrary four-particle cluster state by introducing auxiliary particles, where the receiver performs the unitary operation for recovering the target states. Compared to previous multicast protocols, our scheme reduces resource consumption and operational complexity during cluster state preparation. Additionally, we analyze the system’s fidelity in incoherent environments, providing a more comprehensive understanding of the impact of noise on quantum communication systems.

DOI
10.1088/1402-4896/ad753c

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Abstract The primary aim of this study is to utilize multicast in the preparation of multi-party four-qubit cluster states. In the presence of environment noises, errors may influence the procedure of the particle distribution. To address this challenge, we propose a fault-tolerant scheme to manage the errors within the detectable channel particles. Based on the Bell chain channel, our approach could prepare arbitrary four-particle cluster state by introducing auxiliary particles, where the receiver performs the unitary operation for recovering the target states. Compared to previous multicast protocols, our scheme reduces resource consumption and operational complexity during cluster state preparation. Additionally, we analyze the system’s fidelity in incoherent environments, providing a more comprehensive understanding of the impact of noise on quantum communication systems.
Due to the unavoidable interaction between the quantum channel and its ambient environment, it is difficult to generate and maintain the maximally entanglement. Thus, the research on multiparty information transmission via non-maximally entangled channels is of academic value and general application. Here, we utilize the non-maximally entangled channels to implement two multiparty remote state preparation schemes for transmitting different quantum information from one sender to two receivers synchronously. The first scheme is adopted to transmit two different four-qubit cluster-type entangled states to two receivers with a certain probability. In order to improve success probabilities of such multicast remote state preparation using non-maximally entangled channels, we put forward the second scheme, which deals with the situation that is a synchronous transfer of an arbitrary single-qubit state and an arbitrary two-qubit state from one sender to two receivers. In particular, its success probability can reach 100% in principle, and independent of the entanglement degree of the shared non-maximally entangled channel. Notably, in the second scheme, the auxiliary particle is not required.
We present a strategy for multihop fault-tolerant joint remote state preparation of an arbitrary single-qubit state. To reduce the requirements of the channels, our scheme uses the nonmaximally entangled channel instead of the maximally entangled channel as the quantum channel. However, several typical operational errors such as X, Z, or XZ may occur on the channel qubits when the qubits are distributed from the former node to the next adjacent node. Note that the quantum error correction matrix is considered to deal with the influence of all possible operational errors by the final receiver instead of each intermediate node. Since all the measurement operations in the scheme can be executed in parallel and all the error corrections and the preparation of the target state are handled by the receiver with one unified unitary operation, our scheme significantly reduces both the time delay and the operation complexity and also enhances the implementation efficiency.
In this paper, we propose one multi-hop fault-tolerant teleportation scheme leveraging non-maximally entangled cluster states as the quantum channel, which is crucial for efficient transmission over extended distances. During quantum communication, environmental noise may introduce operational errors between adjacent nodes. In order to uphold the maximum transmission efficiency, error correction operations are exclusively conducted by the ultimate receiver rather than intermediate nodes. Error outcomes from each node can be synchronously relayed to the receiver via the classical channel, effectively diminishing the delays and operational intricacies, thereby significantly bolstering the transmission efficiency. Moreover, we utilize the Quirk simulation software to simulate the teleportation process.
We propose a novel scheme for remote state preparation of an arbitrary three-qubit state with unit success probability, utilizing a nine-qubit cluster-GHZ state without introducing auxiliary qubits. Furthermore, we proceed to investigate the effects of different quantum noises (e.g., amplitude-damping, phase-damping, bit-flip and phase-flip noises) on the systems. The fidelity results of three-qubit target state are presented, which are usually used to illustrate how close the output state is to the target state. To compare the different effects between the four common types of quantum noises, the fidelities under one specific identical target state are also calculated and discussed. It is found that the fidelity of the phase-flip noisy channel drops the fastest through the four types of noisy channels, while the fidelity is found to always maintain at 1 in bit-flip noisy channel.
Abstract Effective propagation of information among multiple users is the purpose of realizing large-scale quantum communication networks. In this paper, multicast protocols for any single, two and three qubits with real amplitude and complex phase information are presented. They were realized using a composite of Greenberger–Horne–Zeilinger states as shared channels. Joint remote state preparation was the main method for completing quantum multicast. At the same time, quantum state tomography of the schemes was carried out on the IBM Quantum platform. The obtained states were compared with the target states by fidelity. The analysis of communication efficiency and noise effects shows that our protocol has advantages in the case of complex coefficients.
Broadcast and multicast protocols are two branches of multi-party quantum communication. Implementing these protocols based on partial entanglement is of great practical importance since maximally entangled channels are not robust due to noise applied by the surrounding environment. Previous research has used global operators (i.e. operators which are applied on the qubits owned by different parties), which contradicts the concept of multi-party communication protocols. In this research, broadcast protocol and multicast protocol with two receivers are proposed using partially entangled channels. Then the protocols are extended to the case with an arbitrary number of receivers. In the proposed protocol, Alice shares a two-qubit maximally entangled state with each receiver, therefore the whole channel is a partially entangled state. Then, the proposed protocol is modified to be secure against eavesdroppers. Also, the effects of phase damping, bit flip, and phase damping noise on the broadcast protocol are examined and compared.