Tripartite Quantum Operation Sharing with a Six-Qubit Absolutely Maximally Entangled State
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Tripartite Quantum Operation Sharing with a Six-Qubit Absolutely Maximally Entangled State Zhanjun Zhang1 · Lei Zhang1 · Bin Zhuge1 · Hao Yuan2,3 · Biaoliang Ye4 Received: 21 October 2020 / Accepted: 2 November 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A three-party scheme for sharing an arbitrary single-qubit operation on a distant target qubit is proposed by utilizing a six-qubit absolutely maximally entangled (AME) state in a given qubit distribution. The security of the proposed scheme is analyzed and ensured. The essential role which the AME state in the given qubit distribution plays in the QOS task is revealed. The important features including scheme determinacy and sharer symmetry are identified. The experimental feasibility of the proposed scheme is simply discussed and confirmed. The scheme is compared with a competing tripartite one proposed by Peng with a same six-qubit AME state but in another qubit distribution (Peng Quant. Inf. Process. 14, 4255, 2015). It is found that this scheme is also applicable and needs less necessary two-qubit operations in contrast to Peng’s. Keywords Quantum operation sharing · Tripartite scheme · Six-qubit absolutely maximally entangled state · Qubit distribution · Operation complexity
1 Introduction In 1993, Bennett et al. [1] creatively invented the very famous quantum state teleportation (QST), where a quantum state in a qudit can be teleported into a distant qudit without remotely transferring any physical qudit. The cost in QST is to consume some shared entanglements and local operations and classical communications. Since then, this topic has attracted much attention in both theoretical and experimental aspects [2–5]. Besides, many new developments revelent to QST have gradually been proposed, too. In 1999, Hillery
Zhanjun Zhang
[email protected] 1
School of Information & Electronic Engineering, Zhejiang Gongshang University, Hangzhou 310018, China
2
School of Physics and Materials Science, Anhui University, Hefei 230039, China
3
School of Electrical & Optoelectronic Engineering, West Anhui University, Luan 237012, China
4
Quantum Information Research Center, Shangrao Normal University, Shangrao 334001, China
International Journal of Theoretical Physics
et al. [6] generalized QST to quantum state sharing (QSS) by incorporating the sharing idea to QST and expanding one state receiver in QST to multi-receivers as cooperative sharers in QSS. In 2001, Huelga et al. [7] first presented the concept of quantum operation teleportation (QOT), which can be taken as a remote control. QST and QOT are similar to some extent. Their main difference is, the object in the former is state while it in the latter is operation. QOT can be viewed as another kind of generalization of QST, too. Both QSS and QOT as the generalizations of QST have been extensively studied in the last three decades [8–35]. Like the generalization of QST to QSS, in 2011 Zhang and Cheung [36] first definitively generalized QOT to quantum operatio
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