Revisiting the operator extension of strong subadditivity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914028708691968 |
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| author | van Luijk, Lauritz Stottmeister, Alexander Wilming, Henrik |
| author_facet | van Luijk, Lauritz Stottmeister, Alexander Wilming, Henrik |
| contents | We give a new proof of the operator extension of the strong subadditivity of von Neumann entropy $ρ_{AB} \otimes σ_{C}^{-1} \leq ρ_{A} \otimes σ_{BC}^{-1}$ by identifying the mathematical structure behind it as Connes' theory of spatial derivatives. This immediately generalizes the inequality to arbitrary inclusions of von Neumann algebras. In the case of standard representations, it reduces to the monotonicity of the relative modular operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03731 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting the operator extension of strong subadditivity van Luijk, Lauritz Stottmeister, Alexander Wilming, Henrik Operator Algebras Mathematical Physics Quantum Physics We give a new proof of the operator extension of the strong subadditivity of von Neumann entropy $ρ_{AB} \otimes σ_{C}^{-1} \leq ρ_{A} \otimes σ_{BC}^{-1}$ by identifying the mathematical structure behind it as Connes' theory of spatial derivatives. This immediately generalizes the inequality to arbitrary inclusions of von Neumann algebras. In the case of standard representations, it reduces to the monotonicity of the relative modular operator. |
| title | Revisiting the operator extension of strong subadditivity |
| topic | Operator Algebras Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2508.03731 |