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Controlled remote state preparation of single-particle state under noisy channels with memory

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Abstract

A novel controlled remote state preparation (CRSP) scheme with three-party is proposed by constructing a new channel. Specifically, the sender can remotely prepare an arbitrary single-particle state at the receiver’s port with the permission of the supervisor. Then, we study the performance of the deterministic controlled remote preparation scheme under two successive uses of Pauli channels with memory, and give general formulas quantifying the fidelity under the correlated Pauli channels. Subsequently, this scheme is analyzed in terms of four types of noise channel with memory. For each type of noise, the average fidelity is calculated as a function of memory and noise parameters. The results demonstrate that for bit-phase flip, depolarizing and two-Pauli noises, memory can increase the average fidelity of CRSP regardless of the noise parameter. In the case of bit-phase flip noise and phase-damping noise, the memory does not affect the CRSP average fidelity because the average fidelity is independent of memory parameter. However, for BB84 noise, under the noisy strength \(p\in [0,0.5]\), when the memory parameter increases, the average fidelity also increases; while the average fidelity decreases with the increase in the memory parameter under the noise parameter \(p\in (0,5,1]\). Finally, it is pointed out that our scheme is safe, and also feasible for the experimental implementation and supervisor’s control.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No.11671284), Natural Science Foundation of Sichuan Province (No.2022NSFSC0534), Key project of Sichuan Normal University (No.XKZX-02), Major Science and Technology Application Demonstration Project in Chengdu (No.2021-YF09-0116-GX).

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Author notes

  1. Zhen Yang, Liang Tang and Ming-Qiang Bai have contributed equally to this work.

Authors and Affiliations

  1. The school of Mathematics and Statistics, Yili Normal University, Yili, 835000, Xinjiang, China

    Jia-Yin Peng

  2. Institute of Intelligent Information and Quantum Information, Sichuan Normal University, Chengdu, 610011, Sichuan, China

    Jia-Yin Peng, Zhen Yang & Ming-Qiang Bai

  3. National-Local Joint Engineering Laboratory of System Credibility Automatic Verification, Research Center of Sichuan Normal University, Chengdu, 610011, Sichuan, China

    Jia-Yin Peng, Zhen Yang & Ming-Qiang Bai

  4. School of Mathematics and Information Science, Xihua University, Chengdu, 610011, Sichuan, China

    Liang Tang

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  1. Jia-Yin Peng
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Correspondence to Ming-Qiang Bai.

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Peng, JY., Yang, Z., Tang, L. et al. Controlled remote state preparation of single-particle state under noisy channels with memory. Quantum Inf Process 22, 145 (2023). https://doi.org/10.1007/s11128-023-03893-7

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