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arXiv · 2406.17299

Measuring quantum relative entropy with finite-size effect

Masahito Hayashi
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Abstract

We study the estimation of relative entropy $D(\rho\|\sigma)$ when $\sigma$ is known. We show that the Cram\'{e}r-Rao type bound equals the relative varentropy. Our estimator attains the Cram\'{e}r-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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Masahito Hayashi. 2024-06-25. Measuring quantum relative entropy with finite-size effect. https://doi.org/10.22331/q-2025-05-05-1725

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