用有限尺寸效应测量量子相对熵

IF 5.1 2区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Quantum Pub Date : 2025-05-05 DOI:10.22331/q-2025-05-05-1725

Masahito Hayashi

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引用次数: 0

摘要

当$\sigma$已知时，我们研究相对熵$D(\rho\|\sigma)$的估计。我们证明了cram - rao型界等于相对异向性。当维度$d$固定时，我们的估计器达到cram r- rao类型边界。当维数$d$增加时，也实现了样例复杂度$O(d^2)$。当$\sigma$是完全混合状态时，这个示例复杂性是最佳的。而且，它有时间复杂度$O(d^6 polylog~d)$。我们提出的估计器在这两种情况下都能统一工作。

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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 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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来源期刊

Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)

CiteScore

9.20

自引率

10.90%

发文量

241

审稿时长

16 weeks

期刊介绍： Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.