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描述一个不确定性图和基克伍德-迪拉克非经典性基于离散的里埃变换
Ying-Hui Yang1, Bing-Bing Zhang1, Xiao-Li Wang1
1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China.
Entropy (Basel, Switzerland)
|July 29, 2023
概括
本研究探讨了在d维系统中使用离散里埃变换 (DFT) 的不确定性图和柯克伍德-迪拉克 (KD) 非经典性. 研究人员确定了不确定性图中的"洞"的特定区域,并为KD非经典性猜测提供了新的证明.
科学领域:
- 量子信息理论就是量子信息理论.
- 量子力学就是量子力学.
- 数学物理学的数学物理.
背景情况:
- 柯克伍德-迪拉克 (KD) 分布为量子状态提供相空间表示.
- 量子系统中的非经典性是量子行为的关键指标,与经典物理学不同.
- 离散里埃转换 (DFT) 是信号处理和量子力学中的一个基本工具,使基础转换成为可能.
研究的目的:
- 为了研究离散里埃变换 (DFT) 矩阵的不确定性图的结构.
- 在d维系统中,在这些不确定性图中描述"洞"区域.
- 为了提供一个替代的证据,推测关于Kirkwood-Dirac (KD) 非古典性来自DFT.
主要方法:
- 对DFT矩阵的不确定性图的分析,作为两个基数 (A和B) 之间的过渡矩阵.
- 检查 (nA,nB) 平面,其中nA和nB代表每个基数中的元素数.
- 基于DFT的特性,开发一种新的KD非经典性的证明.
主要成果:
- 证明DFT矩阵的不确定性图中没有"洞"在nA + nB ≥ d + 1的区域.
- 确定存在"漏洞"的特定区域,即在nA + nB = d + 1直线下方和超标 nA * nB = d以上.
- 与DFT相关的KD非古典性猜测的另一个证明.
结论:
- 该研究澄清了与DFT相关的不确定性图的几何结构.
- 这些发现有助于理解量子系统中非经典性的条件.
- 这项工作为DFT和KD非经典性之间的关系提供了新的视角.
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