Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2211.13372 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915290038665216 |
|---|---|
| author | Lin, Ting-Chun Kim, Isaac H. Hsieh, Min-Hsiu |
| author_facet | Lin, Ting-Chun Kim, Isaac H. Hsieh, Min-Hsiu |
| contents | Let $S(ρ)$ be the von Neumann entropy of a density matrix $ρ$. Weak monotonicity asserts that $S(ρ_{AB}) - S(ρ_A) + S(ρ_{BC}) - S(ρ_C)\geq 0$ for any tripartite density matrix $ρ_{ABC}$, a fact that is equivalent to the strong subadditivity of entropy. We prove an operator inequality, which, upon taking an expectation value with respect to the state $ρ_{ABC}$, reduces to the weak monotonicity inequality. Generalizations of this inequality to the one involving two independent density matrices, as well as their Rényi-generalizations, are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_13372 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A new operator extension of strong subadditivity of quantum entropy Lin, Ting-Chun Kim, Isaac H. Hsieh, Min-Hsiu Quantum Physics Mathematical Physics Let $S(ρ)$ be the von Neumann entropy of a density matrix $ρ$. Weak monotonicity asserts that $S(ρ_{AB}) - S(ρ_A) + S(ρ_{BC}) - S(ρ_C)\geq 0$ for any tripartite density matrix $ρ_{ABC}$, a fact that is equivalent to the strong subadditivity of entropy. We prove an operator inequality, which, upon taking an expectation value with respect to the state $ρ_{ABC}$, reduces to the weak monotonicity inequality. Generalizations of this inequality to the one involving two independent density matrices, as well as their Rényi-generalizations, are also presented. |
| title | A new operator extension of strong subadditivity of quantum entropy |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2211.13372 |