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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.08000 |
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| _version_ | 1866917972670414848 |
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| author | Moraes, Gabriel L. Angelo, Renato M. Costa, Ana C. S. |
| author_facet | Moraes, Gabriel L. Angelo, Renato M. Costa, Ana C. S. |
| contents | Correlations play a pivotal role in various fields of science, particularly in quantum mechanics, yet their proper quantification remains a subject of debate. In this work, we aim to discuss the challenge of defining a reliable measure of total correlations. We first outline essential properties that an effective correlation measure should satisfy and review existing measures, including quantum mutual information, the p-norm of the correlation matrix, and the recently defined quantum Pearson correlation coefficient. Additionally, we introduce new measures based on Rényi and Tsallis relative entropies, as well as the Kullback-Leibler divergence. Our analysis reveals that while quantum mutual information, the p-norm, and the Pearson measure exhibit equivalence for two-qubit systems, they all suffer from an ordering problem. Despite criticisms regarding its reliability, we argue that quantum mutual information remains a valid measure of total correlations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Axiomatic approach to measures of total correlations Moraes, Gabriel L. Angelo, Renato M. Costa, Ana C. S. Quantum Physics Correlations play a pivotal role in various fields of science, particularly in quantum mechanics, yet their proper quantification remains a subject of debate. In this work, we aim to discuss the challenge of defining a reliable measure of total correlations. We first outline essential properties that an effective correlation measure should satisfy and review existing measures, including quantum mutual information, the p-norm of the correlation matrix, and the recently defined quantum Pearson correlation coefficient. Additionally, we introduce new measures based on Rényi and Tsallis relative entropies, as well as the Kullback-Leibler divergence. Our analysis reveals that while quantum mutual information, the p-norm, and the Pearson measure exhibit equivalence for two-qubit systems, they all suffer from an ordering problem. Despite criticisms regarding its reliability, we argue that quantum mutual information remains a valid measure of total correlations. |
| title | Axiomatic approach to measures of total correlations |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2412.08000 |