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Revisiting the operator extension of strong subadditivity
by Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming
Submission summary
| Authors (as registered SciPost users): | Alexander Stottmeister |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2508.03731v3 (pdf) |
| Date submitted: | Sept. 19, 2025, 12:06 p.m. |
| Submitted by: | Alexander Stottmeister |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We give a new proof of the operator extension of the strong subadditivity of von Neumann entropy $\rho_{AB} \otimes \sigma_{C}^{-1} \leq \rho_{A} \otimes \sigma_{BC}^{-1}$ 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.
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Current status:
In refereeing