Measuring quantum relative entropy with finite-size effect
We study the estimation of relative entropy $D(\rho\|\sigma)$ when $\sigma$ is known. We show that the Cramér-Rao type bound equals the relative varentropy. Our estimator attains the Cramér-Rao type bound when the dimension $d$ is fixed. It also achieves the sample complexity $O(d^2)$ when the dimen...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-05-05-1725/pdf/ |
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| _version_ | 1849722746594918400 |
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| author | Masahito Hayashi |
| author_facet | Masahito Hayashi |
| author_sort | Masahito Hayashi |
| collection | DOAJ |
| description | We study the estimation of relative entropy $D(\rho\|\sigma)$ when $\sigma$ is known. We show that the Cramér-Rao type bound equals the relative varentropy. Our estimator attains the Cramér-Rao type bound when the dimension $d$ is fixed. It also achieves the sample complexity $O(d^2)$ when the dimension $d$ increases. This sample complexity is optimal when $\sigma$ is the completely mixed state. Also, it has time complexity $O(d^6 polylog~d)$. Our proposed estimator unifiedly works under both settings. |
| format | Article |
| id | doaj-art-17d7615d4f0d435589ffd88cebc5baaf |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-17d7615d4f0d435589ffd88cebc5baaf2025-08-20T03:11:14ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-05-019172510.22331/q-2025-05-05-172510.22331/q-2025-05-05-1725Measuring quantum relative entropy with finite-size effectMasahito HayashiWe study the estimation of relative entropy $D(\rho\|\sigma)$ when $\sigma$ is known. We show that the Cramér-Rao type bound equals the relative varentropy. Our estimator attains the Cramér-Rao type bound when the dimension $d$ is fixed. It also achieves the sample complexity $O(d^2)$ when the dimension $d$ increases. This sample complexity is optimal when $\sigma$ is the completely mixed state. Also, it has time complexity $O(d^6 polylog~d)$. Our proposed estimator unifiedly works under both settings.https://quantum-journal.org/papers/q-2025-05-05-1725/pdf/ |
| spellingShingle | Masahito Hayashi Measuring quantum relative entropy with finite-size effect Quantum |
| title | Measuring quantum relative entropy with finite-size effect |
| title_full | Measuring quantum relative entropy with finite-size effect |
| title_fullStr | Measuring quantum relative entropy with finite-size effect |
| title_full_unstemmed | Measuring quantum relative entropy with finite-size effect |
| title_short | Measuring quantum relative entropy with finite-size effect |
| title_sort | measuring quantum relative entropy with finite size effect |
| url | https://quantum-journal.org/papers/q-2025-05-05-1725/pdf/ |
| work_keys_str_mv | AT masahitohayashi measuringquantumrelativeentropywithfinitesizeeffect |