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Strong subadditivity of quantum mechanical entropy for semifinite von Neumann algebras

Volume 257 / 2021

Hanna Podsędkowska Studia Mathematica 257 (2021), 71-85 MSC: Primary 81Q10. DOI: 10.4064/sm190929-7-2 Published online: 31 August 2020

Abstract

We show that for Segal entropy defined for states on an arbitrary von Neumann algebra with normal faithful semifinite trace, strong subadditivity holds. We also prove some other related properties of this generalized entropy, in particular the concavity of $S(\rho _{12})-S(\rho _2)$, the subadditivity of entropy, and a generalization of the Araki–Lieb inequality.

Authors

  • Hanna PodsędkowskaFaculty of Mathematics and Computer Sciences
    University of Łódź
    Banacha 22
    90-238 Łódź, Poland
    e-mail

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