Pre-schmidt mode parameters in quantum entanglement
We wrote this paper to study in detail the mathematical methods used in deriving the parameters p'_1, p'_2, x'_1, x2_2, M, K and exp(2n) 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 A_K in quantum enta...
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Akademi Sains Malaysia
2024
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my.upm.eprints.1089542024-05-27T02:07:22Z http://psasir.upm.edu.my/id/eprint/108954/ Pre-schmidt mode parameters in quantum entanglement Murugaya, Tamil Selvam Mohd Shah, Nurisya Said Husain, Sharifah Kartini We wrote this paper to study in detail the mathematical methods used in deriving the parameters p'_1, p'_2, x'_1, x2_2, M, K and exp(2n) 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 A_K 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 K and exp(2n) using the matrices’ determinants and eigenvalues. With these rationales in deriving the parameters K and exp(2n) 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. Akademi Sains Malaysia 2024 Article PeerReviewed Murugaya, Tamil Selvam and Mohd Shah, Nurisya and Said Husain, Sharifah Kartini (2024) Pre-schmidt mode parameters in quantum entanglement. ASM Science Journal, 18. pp. 1-14. ISSN 1823-6782 https://www.akademisains.gov.my/asmsj/article/pre-schmidt-mode-parameters-in-quantum-entanglement/ 10.32802/asmscj.2023.1355 |
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| description |
We wrote this paper to study in detail the mathematical methods used in deriving the parameters p'_1, p'_2, x'_1, x2_2, M, K and exp(2n) 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 A_K 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 K and exp(2n) using the matrices’ determinants and eigenvalues. With these rationales in deriving the parameters K and exp(2n) 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. |
| format |
Article |
| author |
Murugaya, Tamil Selvam Mohd Shah, Nurisya Said Husain, Sharifah Kartini |
| spellingShingle |
Murugaya, Tamil Selvam Mohd Shah, Nurisya Said Husain, Sharifah Kartini Pre-schmidt mode parameters in quantum entanglement |
| author_facet |
Murugaya, Tamil Selvam Mohd Shah, Nurisya Said Husain, Sharifah Kartini |
| author_sort |
Murugaya, Tamil Selvam |
| title |
Pre-schmidt mode parameters in quantum entanglement |
| title_short |
Pre-schmidt mode parameters in quantum entanglement |
| title_full |
Pre-schmidt mode parameters in quantum entanglement |
| title_fullStr |
Pre-schmidt mode parameters in quantum entanglement |
| title_full_unstemmed |
Pre-schmidt mode parameters in quantum entanglement |
| title_sort |
pre-schmidt mode parameters in quantum entanglement |
| publisher |
Akademi Sains Malaysia |
| publishDate |
2024 |
| url |
http://psasir.upm.edu.my/id/eprint/108954/ https://www.akademisains.gov.my/asmsj/article/pre-schmidt-mode-parameters-in-quantum-entanglement/ |
| _version_ |
1800721408003670016 |
| score |
13.251813 |