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Bidirectional and cyclic quantum dense coding in a high-dimension system

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Abstract

In light of quantum dense coding in the case of high-dimension quantum states between two parties, by introducing additional local operations for encoding, we propose a brand-new bidirectional quantum dense coding scheme, in which two legitimate agents can simultaneously transmit their different encoded messages to each other. In addition, we present a bidirectional quantum dense coding scheme with a control by virtue of the generalized Hadamard transformation. We show how to implement the cyclic quantum dense coding in an arbitrary high dimension where Alice can transfer her encoded messages \(n_1m_1\) to Bob; meanwhile, Bob can transfer his encoded messages \(n_2m_2\) to Charlie and Charlie can also transfer his encoded messages \(n_3m_3\) to Alice in both clockwise and counterclockwise directions. We can also generalize the cyclic scheme to system having \(n\ge 3\) agents. Thereby, our scheme can realize dense coding in quantum information networks with n agents in arbitrary directions.

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Acknowledgements

The authors thank all of the editors and reviewers for their valuable suggestions, which have substantially improved this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 11671284), Sichuan Province Science and Technology Support Program (Grant No. 2017JY0197). The Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (Grant No. 2018QYJ02).

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Authors and Affiliations

  1. School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 611756, China

    Xue Yang

  2. School of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, China

    Xue Yang, Ming-qiang Bai, Zhi-wen Mo & Yi Xiang

  3. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610066, China

    Xue Yang, Ming-qiang Bai, Zhi-wen Mo & Yi Xiang

  4. School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, 643000, China

    Yi Xiang

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  1. Xue Yang
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Yang, X., Bai, Mq., Mo, Zw. et al. Bidirectional and cyclic quantum dense coding in a high-dimension system. Quantum Inf Process 19, 43 (2020). https://doi.org/10.1007/s11128-019-2526-9

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