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Deterministic hierarchical quantum operation sharing with five-qubit partially entangled states

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Abstract

To study quantum remote control in the form of hierarchical quantum sharing, by using a Hadamard gate, control-NOT gates and rotation gates, we construct a five-qubit partially entangled state as quantum channels of quantum remote control. By integrating the ideas of hierarchical quantum state sharing and quantum operation teleportation, we put forward two novel schemes for quadripartite hierarchical sharing a single-qubit quantum operation on a qubit in any sharer’s site with the help of the local operations and classical communication. In each scheme, there is a hierarchy among the receivers concerning powers to reconstruct the conceivable state. Owing to various unitary operations and projective measurements, the unit success probability can always be achieved irrespective of the parameters of the pre-shared partially entangled state as quantum channel. The first scheme is applicable for arbitrary unitary operations, while the other one is valid only if the operation \(\mathcal {U}_d\) (\(d=0,1\)) in question is known to belongs to some restricted sets. Consequently, the latter scheme is more economical in terms of quantum and classical resources, and the local operation complexity involved is also reduced.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11671284), Natural Science Foundation of Sichuan Province (Grant No. 2022NSFSC0534).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yili Normal University, Yili, 835000, People’s Republic of China

    Jia-Yin Peng

  2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610066, People’s Republic of China

    Jia-Yin Peng & Zhen Yang

  3. School of Mathematical Sciences, Sichuan Normal University, Chengdu, 610066, People’s Republic of China

    Jia-Yin Peng & Zhen Yang

  4. School of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641100, Sichuan, People’s Republic of China

    Jia-Yin Peng

  5. School of Science, Xihua University, Chengdu, 610039, People’s Republic of China

    Liang Tang

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  1. Jia-Yin Peng
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Contributions

In fact, all of the authors’ contributions to this paper are important. The specific contributions are as follows. The first author plays a major role in the idea and writes the main content. The second author devotes to all the process of calculation and the language problem. The third author establishes the overall framework of this article.

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Correspondence to Zhen Yang.

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Peng, JY., Tang, L. & Yang, Z. Deterministic hierarchical quantum operation sharing with five-qubit partially entangled states. Quantum Inf Process 22, 265 (2023). https://doi.org/10.1007/s11128-023-03963-w

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