Measuring quantum relative entropy with finite-size effect
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916720982097920 |
|---|---|
| author | Hayashi, Masahito |
| author_facet | Hayashi, Masahito |
| contents | We study the estimation of relative entropy $D(ρ\|σ)$ when $σ$ 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 $σ$ is the completely mixed state. Also, it has time complexity $O(d^6 \polylog d)$. Our proposed estimator unifiedly works under both settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17299 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Measuring quantum relative entropy with finite-size effect Hayashi, Masahito Quantum Physics We study the estimation of relative entropy $D(ρ\|σ)$ when $σ$ 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 $σ$ is the completely mixed state. Also, it has time complexity $O(d^6 \polylog d)$. Our proposed estimator unifiedly works under both settings. |
| title | Measuring quantum relative entropy with finite-size effect |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.17299 |