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Physica Scripta

Bilateral fault-tolerant qudit teleportation in multi-hop quantum networks

Zongyi Li, Yuzhen Wei, Shibei Xue, Min Jiang, Yongcheng Li

Published Apr 4, 2024• 0 citations
Publisher

Abstract

Abstract In this paper, we present one general fault-tolerant multi-hop teleportation scheme for arbitrary unknown qudit system, exploring a strategy for distilling high-dimensional EPR pairs within the operational errors channel, where the introduced auxiliary pairs don’t have to be in high-fidelity. These errors can be detectable and traceable in quantum networks, promising that the accumulation of the operational errors can be rectified by the final receiver during the teleportation, avoiding the error correction implemented by the intermediate nodes. Moreover, we extend the strategy to the non-maximally entangled EPR channels. In the end, we discuss the potential strategy to improve our scheme including eliminating the encoding step for the error correction codes. Even through the operational errors may occur at the repeater nodes, the performance analysis demonstrates that the scheme significantly preserves the valuable entangled resources and reduces the operational complexity, illustrating the robustness to against the operational errors in repeater nodes.

DOI
10.1088/1402-4896/ad3ad9

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Abstract In this paper, we present one general fault-tolerant multi-hop teleportation scheme for arbitrary unknown qudit system, exploring a strategy for distilling high-dimensional EPR pairs within the operational errors channel, where the introduced auxiliary pairs don’t have to be in high-fidelity. These errors can be detectable and traceable in quantum networks, promising that the accumulation of the operational errors can be rectified by the final receiver during the teleportation, avoiding the error correction implemented by the intermediate nodes. Moreover, we extend the strategy to the non-maximally entangled EPR channels. In the end, we discuss the potential strategy to improve our scheme including eliminating the encoding step for the error correction codes. Even through the operational errors may occur at the repeater nodes, the performance analysis demonstrates that the scheme significantly preserves the valuable entangled resources and reduces the operational complexity, illustrating the robustness to against the operational errors in repeater nodes.
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.
Quantum teleportation (QT) provides a useful way to securely transfer unknown quantum state between distant nodes without physically sending the states themselves. In this paper, we present a teleportation scheme of the most general hybrid multi-qudit state via EPR pairs with different dimensions in the chain network. In this structure, the EPR channels shared between neighbor nodes could be distinct, which means that the shared EPR pairs could be different in dimension and the parameters with each other, demonstrating a universality scenario in realistic transmission. In addition, we discuss the condition that can ensure the integrity of the transmitted information with available channel resource, and our scheme could provide a method to solve the resemble problem in the construction of future quantum network.
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.
Abstract Quantum teleportation is one of the key technologies enabling long-distance quantum communication. However, the decoherence in realistic channels makes it difficult to maintain maximal entanglement. Furthermore, the capability to perform high-dimensional unitary operations poses a significant challenge, as not all the nodes in the quantum network possess this ability. Meanwhile, low transmission rates also hinder the development of quantum networks. We propose a flexible multi-hop non-destructive teleportation via non-maximally entangled GHZ channels, where the network is partitioned into upstream and downstream segments. Direct entanglement channels are established via simultaneous entanglement swapping and multi-level hierarchical swapping. Channel modulation is performed by the selected intermediate parties with high-dimensional operational capabilities and auxiliary particles. In this framework, the sender and the receiver are responsible only for information transmission, while other intermediate nodes perform only basic operations, such as Bell-state and Hadamard ( H ) measurements. In this scheme, any intermediate node possesses high-dimensional unitary operation capability, making the teleportation process flexible in terms of node deployment and operational responsibility, thereby reducing the requirements for the communication terminals.
In this paper, we propose a scheme for the multi-hop nondestructive teleportation of an arbitrary single-qudit state via channel modulation performed by one cloud node in a network. Considering the limited quantum technology of the sender, the receiver, and the ordinary intermediate nodes, we assume that there are certain cloud nodes in a quantum network equipped with quantum processing capability of performing high-dimensional multi-qudit unitary operations. In our scheme, N intermediate nodes, involving one cloud node and N − 1 ordinary relay nodes, are connected in a chain through N + 1 different non-maximally entangled Bell pairs. Our scheme reduces the hardware requirement of the terminals, which makes it more flexible and adaptable in a network. In addition, our scheme enables preservation of the original single-qudit state, even if the teleportation fails. Our finding provides a methodology for the multi-hop nondestructive teleportation in a network with limited technical processing capabilities of terminals.
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical qudits in finite-dimensional spin systems. We construct distance-333, distance-555 codewords, and general 2t+12t+12t+1-distance codes that can be implemented using a single physical qudit or a small number of coupled qudits for higher distances, while requiring a Hilbert space dimension significantly smaller than conventional constructions based on multiple logical qubits. Logical operations and error correction protocols can be implemented with polynomial scaling in the number of elementary operations. We further discuss schematic designs for physical implementation and required single-gate fidelities, which are compatible with current spin qudit platforms. This strategy provides a resource-efficient path toward realizing fault-tolerant logical qudits in finite multi-level physical systems.