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High-dimensional bidirectional controlled teleportation based on network coding

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Abstract

Two explicit schemes are designed to illustrate bidirectional controlled teleportation in a fair and practical manner. One is a symmetric scheme for single-qutrit states. The other is an asymmetric scheme for single- and two-qutrit states. Then, we extend three-dimensional system to high-dimensional system and come up with a universal scheme for arbitrary \(n_1\)- and \(n_2\)-qudit states by using a \((2n_1+2n_2+1)\)-qudit entangled state as the quantum channel, where \(n_1\le n_2\). The senders and the controller need to perform general Bell basis measurement and Z basis measurement, respectively. According to their measurement results, the receivers can reestablish the initial states simultaneously by performing single-qudit recovery operations which are derived by a general formula. It is worth mentioning that \(2n_1+1\) dit classical communication cost is saved at the controller’s broadcast channel with the aid of network coding. Moreover, we consider the effect of two-type high-dimensional decoherence noises: dit-flip noise and d-phase-flip noise.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61201253, 62172341, 62172196, 62272208), Open Foundation of State Key Laboratory of Networking and Switching Technology (Beijing University of Posts and Telecommunications) (No. SKLNST-2020-2-02).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University, Kaifeng, 475004, China

    Songya Ma, Mengyao He & Junli Jiang

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Songya Ma

  3. Henan Engineering Research Center for Artificial Intelligence Theory and Algorithms, Henan University, Kaifeng, 475004, China

    Songya Ma

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  1. Songya Ma
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Ma, S., He, M. & Jiang, J. High-dimensional bidirectional controlled teleportation based on network coding. Quantum Inf Process 21, 398 (2022). https://doi.org/10.1007/s11128-022-03744-x

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