Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification
Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demons...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/6892178 |
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| author | Jonas Maziero |
| author_facet | Jonas Maziero |
| author_sort | Jonas Maziero |
| collection | DOAJ |
| description | Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this paper, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell-Mann matrices and to compute the optimized and unoptimized versions of associated Bloch’s vectors and correlation matrix in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords. |
| format | Article |
| id | doaj-art-8b8239075da04e77a8b7c923ef2326c7 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8b8239075da04e77a8b7c923ef2326c72025-02-03T06:06:52ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/68921786892178Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord QuantificationJonas Maziero0Departamento de Física, Centro de Ciências Naturais e Exatas, Universidade Federal de Santa Maria, Avenida Roraima 1000, 97105-900 Santa Maria, RS, BrazilCoherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this paper, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell-Mann matrices and to compute the optimized and unoptimized versions of associated Bloch’s vectors and correlation matrix in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords.http://dx.doi.org/10.1155/2016/6892178 |
| spellingShingle | Jonas Maziero Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification Advances in Mathematical Physics |
| title | Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification |
| title_full | Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification |
| title_fullStr | Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification |
| title_full_unstemmed | Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification |
| title_short | Computing Coherence Vectors and Correlation Matrices with Application to Quantum Discord Quantification |
| title_sort | computing coherence vectors and correlation matrices with application to quantum discord quantification |
| url | http://dx.doi.org/10.1155/2016/6892178 |
| work_keys_str_mv | AT jonasmaziero computingcoherencevectorsandcorrelationmatriceswithapplicationtoquantumdiscordquantification |