中国物理B ›› 2023, Vol. 32 ›› Issue (8): 80307-080307.doi: 10.1088/1674-1056/acd5c5

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Algorithm for evaluating distance-based entanglement measures

Yixuan Hu(胡奕轩)1, Ye-Chao Liu(刘烨超)2,1,†, and Jiangwei Shang(尚江伟)1,‡   

  1. 1. Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China;
    2. Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany
  • 收稿日期:2023-03-31 修回日期:2023-05-09 接受日期:2023-05-16 发布日期:2023-07-27
  • 通讯作者: Ye-Chao Liu, Jiangwei Shang E-mail:ye-chao.liu@uni-siegen.de;jiangwei.shang@bit.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos.12175014 and 92265115) and the National Key Research and Development Program of China (Grant No.2022YFA1404900). Y. C. Liu is also supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, project numbers 447948357 and 440958198) and the Sino-German Center for Research Promotion (Project M-0294).

Algorithm for evaluating distance-based entanglement measures

Yixuan Hu(胡奕轩)1, Ye-Chao Liu(刘烨超)2,1,†, and Jiangwei Shang(尚江伟)1,‡   

  1. 1. Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China;
    2. Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany
  • Received:2023-03-31 Revised:2023-05-09 Accepted:2023-05-16 Published:2023-07-27
  • Contact: Ye-Chao Liu, Jiangwei Shang E-mail:ye-chao.liu@uni-siegen.de;jiangwei.shang@bit.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos.12175014 and 92265115) and the National Key Research and Development Program of China (Grant No.2022YFA1404900). Y. C. Liu is also supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, project numbers 447948357 and 440958198) and the Sino-German Center for Research Promotion (Project M-0294).

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摘要： Quantifying entanglement in quantum systems is an important yet challenging task due to its NP-hard nature. In this work, we propose an efficient algorithm for evaluating distance-based entanglement measures. Our approach builds on Gilbert's algorithm for convex optimization, providing a reliable upper bound on the entanglement of a given arbitrary state. We demonstrate the effectiveness of our algorithm by applying it to various examples, such as calculating the squared Bures metric of entanglement as well as the relative entropy of entanglement for GHZ states, W states, Horodecki states, and chessboard states. These results demonstrate that our algorithm is a versatile and accurate tool that can quickly provide reliable upper bounds for entanglement measures.

关键词: quantum information, entanglement measurement, convex optimization

Abstract: Quantifying entanglement in quantum systems is an important yet challenging task due to its NP-hard nature. In this work, we propose an efficient algorithm for evaluating distance-based entanglement measures. Our approach builds on Gilbert's algorithm for convex optimization, providing a reliable upper bound on the entanglement of a given arbitrary state. We demonstrate the effectiveness of our algorithm by applying it to various examples, such as calculating the squared Bures metric of entanglement as well as the relative entropy of entanglement for GHZ states, W states, Horodecki states, and chessboard states. These results demonstrate that our algorithm is a versatile and accurate tool that can quickly provide reliable upper bounds for entanglement measures.

Key words: quantum information, entanglement measurement, convex optimization

中图分类号:  (Quantum information)

  • 03.67.-a
03.67.Mn (Entanglement measures, witnesses, and other characterizations) 02.60.Pn (Numerical optimization)