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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (2): 207-213.doi: 10.3969/j.issn.1005-3085.2021.02.005

• • 上一篇    下一篇

多体量子纯态纠缠测量的凹性

韦娜娜,   王   震,   章培军   

  1. 西京学院理学院，西安  710123
  • 收稿日期:2019-05-07 接受日期:2020-06-26 出版日期:2021-04-15 发布日期:2022-11-08
  • 基金资助:
    国家自然科学基金 (11726624; 11726623)；陕西省自然科学基础研究计划项目 (2020JM-646)；陕西省创新能力支撑计划项目 (2018GHJD-21)；陕西省教育厅科学研究计划项目 (20JK0967)；西安市科技计划项目 (2019218414GXRC020CG021-GXYD20.3)；西京学院校科研基金项目 (XJ200103; XJ200106).

The Concavity of Multi-body Quantum Entanglement Measurements

WEI Na-na,   WANG Zhen,   ZHANG Pei-jun   

  1. School of Science, Xijing University, Xi'an 710123
  • Received:2019-05-07 Accepted:2020-06-26 Online:2021-04-15 Published:2022-11-08
  • Supported by:
    The National Natural Science Foundation of China (11726624; 11726623); the Natural Science Basic Research Program of Shaanxi Province (2020JM-646); the Innovation Capability Support Program of Shaanxi (2018GHJD-21); the Science Research Plan of the Education Department of Shaanxi Province (20JK0967); the Science and Technology Plan Projects of Xi'an (2019218414GXRC020CG021-GXYD20.3); the Research Foundation of Xijing University (XJ200103; XJ200106).

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摘要： 在量子信息和量子计算中，量子纠缠是最主要的物理资源．本文基于两体量子纠缠测量的基础理论，讨论多体量子纯态纠缠测量的重要性质．首先，利用Schmidt分解方法得到两体量子纯态纠缠测量的凹性．其次，利用拓扑分析与不等式理论得到凸组合的多体量子纯态纠缠测量的凹性．最后，通过控制论与Schur-凸函数理论对任意两体量子纯态纠缠测量的上界进行了精确的估算．本文得到的凹性更加成功地描述了拓扑物态的Kitaev蜂巢模型中的拓扑序，扩大了问题的讨论范围，进而将应用于拓扑量子计算和量子精密测量中．

关键词: 量子态, 纯态, 混合态, 纠缠测量

Abstract: Quantum entanglement is the most important physical resource in quantum information and quantum computation. Based on the basic theory of two-body quantum entanglement measurement, the important properties of the entanglement measurement of multi-body quantum pure state is discussed by the topological analysis and control theory in this paper. Firstly, the concavity of entanglement measurement of two-body quantum pure states is obtained by Schmidt decomposition. Secondly, the concavity of the convex combination of the entanglement measurement of multi-body quantum pure states is considered by the topological analysis and inequality theory. Finally, the upper bound of two-body quantum pure states is precisely studied by the control theory and Schur convex function. The concavity is analytic and able to calculate, and the topological order of states is described more successfully in the Kitaev model. Therefore, this work is broadened to topological quantum computation and quantum precision measurement.

Key words: quantum state, pure state, mixed state, entanglement measurement

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