量子纠缠中的前施密特模式参数

Q4 Multidisciplinary

ASM Science Journal Pub Date : 2024-01-04 DOI:10.32802/asmscj.2023.1355

Tamil Selvam Murugaya, Nurisya Mohd Shah, Sharifah Kartini Said Husain

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引用次数: 0

摘要

我们撰写本文的目的是详细研究 Han 等人（1999 年）、Makarov（2018a）、Han 等人（1993 年）和 Han 等人（1995 年）的研究论文中推导参数𝑝′1、𝑝′2、𝑥𝑥′1、𝑥′2、𝑀𝑀、𝑒𝑒2𝜂𝜂时所使用的数学方法。(1999）、Makarov（2018a）、Han 等（1993）和 Han 等（1995）的研究论文中找到了量子纠缠中的施密特模式𝛬𝛬𝑘𝑘。在此，我们进行了全面的分析和计算，以探索这些参数在二耦合和三耦合谐振子中存在的理由。研究中应用了多种数学方法，从多项式和线性代数到三角学和勾股定理。我们利用矩阵的行列式和特征值找到了参数(⑪)和(𝑒)2𝜂𝜂。根据上述推导二耦合谐波振荡器研究论文中的参数 "廓清 "和 "廓清 "2𝜂𝜂的原理，我们为三耦合谐波振荡器制定了类似的参数，作为我们研究的结论。

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Pre-Schmidt Mode Parameters in Quantum Entanglement

We wrote this paper to study in detail the mathematical methods used in deriving the parameters 𝑝𝑝′1, 𝑝𝑝′2, 𝑥𝑥′1, 𝑥𝑥′2, 𝑀𝑀, 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 in the research papers by Han et al. (1999), Makarov (2018a), Han et al. (1993), and Han et al. (1995) to find the Schmidt modes 𝛬𝛬𝑘𝑘 in quantum entanglement. Here, we have analysed and developed a thorough calculation in exploring the rationales behind the existence of these parameters in two and three-coupled harmonic oscillators. Various mathematical approaches were applied in the study, ranging from polynomials and linear algebra to trigonometry and the Pythagorean theorem. We found the parameters 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 using the matrices’ determinants and eigenvalues. With these rationales in deriving the parameters 𝐾𝐾 and 𝑒𝑒2𝜂𝜂 in the research papers for the two-coupled harmonic oscillators, we have formulated similar parameters for three-coupled harmonic oscillators as the conclusion of our study.

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来源期刊

ASM Science Journal Multidisciplinary-Multidisciplinary

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The ASM Science Journal publishes advancements in the broad fields of medical, engineering, earth, mathematical, physical, chemical and agricultural sciences as well as ICT. Scientific articles published will be on the basis of originality, importance and significant contribution to science, scientific research and the public. Scientific articles published will be on the basis of originality, importance and significant contribution to science, scientific research and the public. Scientists who subscribe to the fields listed above will be the source of papers to the journal. All articles will be reviewed by at least two experts in that particular field.