中国物理B ›› 2025, Vol. 34 ›› Issue (8): 80302-080302.doi: 10.1088/1674-1056/adeb5d

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Optimal convex approximations of qubit states based on l1-norm of coherence

Li-Qiang Zhang(张立强)1,†, Yan-Dong Du(杜彦东)1, and Chang-Shui Yu(于长水)2,3,‡   

  1. 1 School of Physics and Electronic Engineering, Shanxi Normal University, Taiyuan 030031, China;
    2 School of Physics, Dalian University of Technology, Dalian 116024, China;
    3 DUT-BSU Joint Institute, Dalian University of Technology, Dalian 116024, China
  • 收稿日期:2025-04-16 修回日期:2025-06-22 接受日期:2025-07-03 出版日期:2025-07-17 发布日期:2025-08-08
  • 通讯作者: Li-Qiang Zhang, Chang-Shui Yu E-mail:zhangliqiang@sxnu.edu.cn;ycs@dlut.edu.cn
  • 基金资助:
    Project supported by the Fundamental Research Projects of Shanxi Province (Grant No. 202203021222225), the National Natural Science Foundation of China (Grant Nos. 12175029, 12011530014, and 11775040), and the Key Research and Development Project of Liaoning Province (Grant No. 2020JH2/10500003).

Optimal convex approximations of qubit states based on l1-norm of coherence

Li-Qiang Zhang(张立强)1,†, Yan-Dong Du(杜彦东)1, and Chang-Shui Yu(于长水)2,3,‡   

  1. 1 School of Physics and Electronic Engineering, Shanxi Normal University, Taiyuan 030031, China;
    2 School of Physics, Dalian University of Technology, Dalian 116024, China;
    3 DUT-BSU Joint Institute, Dalian University of Technology, Dalian 116024, China
  • Received:2025-04-16 Revised:2025-06-22 Accepted:2025-07-03 Online:2025-07-17 Published:2025-08-08
  • Contact: Li-Qiang Zhang, Chang-Shui Yu E-mail:zhangliqiang@sxnu.edu.cn;ycs@dlut.edu.cn
  • Supported by:
    Project supported by the Fundamental Research Projects of Shanxi Province (Grant No. 202203021222225), the National Natural Science Foundation of China (Grant Nos. 12175029, 12011530014, and 11775040), and the Key Research and Development Project of Liaoning Province (Grant No. 2020JH2/10500003).

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摘要： Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory, offering critical guidance for experimental implementations. In this paper, we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the ${l_1}$-norm of coherence of the target quantum state, striving to make the prepared state and the target state as similar as possible. Here, we present the analytical solution for the optimal distance for any $N$ given quantum states. We find that the optimal approximation problem for any $N>4$ quantum states can be transformed into an optimal approximation problem for no more than four quantum states, which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation. Ultimately, a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach.

关键词: quantum information processing, quantum resource theory, quantum coherence, optimal convex approximations

Abstract: Determining the minimal distance between the target state and the convex combination of given states is a fundamental problem in quantum resource theory, offering critical guidance for experimental implementations. In this paper, we embark on an in-depth exploration of the use of a quantum state prepared by the convex combination of given qubit states to optimally approximate the ${l_1}$-norm of coherence of the target quantum state, striving to make the prepared state and the target state as similar as possible. Here, we present the analytical solution for the optimal distance for any $N$ given quantum states. We find that the optimal approximation problem for any $N>4$ quantum states can be transformed into an optimal approximation problem for no more than four quantum states, which not only significantly streamlines the problem but also proves advantageous for laboratories in terms of material conservation. Ultimately, a one-to-one comparison between the analytical and numerical solutions verifies the effectiveness of our approach.

Key words: quantum information processing, quantum resource theory, quantum coherence, optimal convex approximations

中图分类号:  (Quantum information)

  • 03.67.-a
03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.65.Fd (Algebraic methods)