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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 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 |
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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.
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Received: 16 April 2025
Revised: 22 June 2025
Accepted manuscript online: 03 July 2025
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PACS:
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03.67.-a
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(Quantum information)
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03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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03.65.Fd
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(Algebraic methods)
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| Fund: 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). |
Corresponding Authors:
Li-Qiang Zhang, Chang-Shui Yu
E-mail: zhangliqiang@sxnu.edu.cn;ycs@dlut.edu.cn
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Cite this article:
Li-Qiang Zhang(张立强), Yan-Dong Du(杜彦东), and Chang-Shui Yu(于长水) Optimal convex approximations of qubit states based on l1-norm of coherence 2025 Chin. Phys. B 34 080302
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