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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| Main Author: | |
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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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| Summary: | 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. |
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| ISSN: | 2521-327X |