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. 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
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.
Fund: 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).
Yixuan Hu(胡奕轩), Ye-Chao Liu(刘烨超), and Jiangwei Shang(尚江伟) Algorithm for evaluating distance-based entanglement measures 2023 Chin. Phys. B 32 080307
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