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Discussion on the initial states of controlled bidirectional quantum secure direct communication

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Abstract

In many communication scenarios, it is necessary to involve a third party for control and supervision. In the context of controlled bidirectional quantum secure direct communication (CBQSDC) protocols, the transmission of secret messages between two legitimate users is only permitted with the explicit permission of a controller. To address the issue of controlled communication, a CBQSDC protocol (CLYH2015) utilizing Bell states was proposed in the paper (Quant Inf Process 14, 3515–3522, 2015). Bell states have been widely recognized for their significance in the field of quantum secure direct communication. In a subsequent study published in (Quant Inf Process 16, 147, 2017), the research examined whether CLYH2015 protocol strictly requires the initial states to be Bell states. The conclusion drawn from this investigation is that CLYH2015 protocol working properly necessitates the use of Bell states as initial states. To explore alternative possibilities for the initial states in CLYH2015 protocol, a class of CBQSDC protocols employing the generalized Bell states (GBell states), \(a\arrowvert 00\rangle + b\arrowvert 11\rangle \), \({\bar{b}}\arrowvert 00\rangle -{\bar{a}}\arrowvert 11\rangle \), \(a\arrowvert 01\rangle + b\arrowvert 10\rangle \), and \({\bar{b}}\arrowvert 01\rangle -{\bar{a}}\arrowvert 10\rangle \), are designed where a and b are complex numbers with \(|a|=|b|=\frac{1}{\sqrt{2}}\), \({\bar{a}}\) and \({\bar{b}}\) the conjugate complex numbers of a and b, respectively. The class of designed CBQSDC protocols demonstrates several favorable properties, including resistance against information leakage, intercept-and-resend attacks, measure-resend attacks, as well as robustness against collective attacks. In addition, the unconditional security of the class of designed protocols is proved. Finally, to show the advantages of the class of designed protocols, they are compared with some with some previous closely associated protocols. Interestingly, it is worth noting that the Bell states can be considered a special case of the GBell states when both a and b are real numbers. Consequently, CLYH2015 protocol can be regarded as a particular instance of the designed CBQSDC protocols. This insight implies that the initial states in CLYH2015 protocol can be extended to include the GBell states, rather than being limited solely to the Bell states.

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The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding authors.

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Acknowledgements

This work was supported in part by the Joint Research and Development Fund of Wuyi University, Hong Kong and Macao (No. 2021WGALH16), the National Natural Science Foundations of China (Nos. 61871205 and 11874312), the Innovation Program for Quantum Science and Technology (No. 2021ZD0302900), the Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515012623), the Innovation Project of Department of Education of Guangdong Province of China (No. 2017KTSCX180), the Science and Technology Project of Jiangmen City of China (No. 2021030101270004596), and Special Foundation in Key Fields for Universities of Guangdong Province (2023ZDZX4060).

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Authors and Affiliations

  1. School of Mathematics and Computational Science, Wuyi University, Jiangmen, 529020, China

    Jianfeng Liu, Xiangfu Zou, Ying Chen, Xueying Liang & Jianxiong Wu

  2. Department of Physics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China

    Xin Wang

  3. City University of Hong Kong Shenzhen Research Institute, Shenzhen, 518057, China

    Xin Wang

  4. Faculty of Intelligent Manufacturing, Wuyi University, Jiangmen, 529020, China

    Zhenbang Rong

  5. School of Economics and Management, Wuyi University, Jiangmen, 529020, China

    Zhiming Huang

  6. Peng Cheng Laboratory, Shenzhen, 518000, China

    Shenggen Zheng

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  1. Jianfeng Liu
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Liu, J., Zou, X., Wang, X. et al. Discussion on the initial states of controlled bidirectional quantum secure direct communication. Quantum Inf Process 22, 426 (2023). https://doi.org/10.1007/s11128-023-04178-9

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