Related papers: Revisiting the operator extension of strong subadditivity

Revisiting the operator extension of strong subadditivity

URL: http://arxiv.org/abs/2508.03731v1
Date: Wed, 30 Jul 2025 14:18:43 GMT
Title: Revisiting the operator extension of strong subadditivity
Authors: Lauritz van Luijk, Alexander Stottmeister, Henrik Wilming,
Abstract summary: 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.
Score: 44.99833362998488
License: http://creativecommons.org/licenses/by/4.0/
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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