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arXiv · 1909.02335

Upper bounds for relative entropy of entanglement based on active learning

Shi-Yao Hou·Chenfeng Cao·D. L. Zhou·Bei Zeng
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Abstract

Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its clear geometric meaning, easy compatibility with different system sizes, and various applications in many other related quantity calculations. Lower bounds of $E_R$ were previously found based on distance to the set of positive partial transpose states. We propose a method to calculate upper bounds of $E_R$ based on active learning, a subfield in machine learning, to generate an approximation of the set of separable states. We apply our method to calculate $E_R$ for composite systems of various sizes, and compare with the previous known lower bounds, obtaining promising results. Our method adds a reliable tool for entanglement measure calculation and deepens our understanding for the structure of separable states.

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Shi-Yao Hou, Chenfeng Cao, D. L. Zhou, Bei Zeng. 2020-07-07. Upper bounds for relative entropy of entanglement based on active learning. https://doi.org/10.1088/2058-9565%2Fabb412

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