Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings

Marius Junge, Nicholas Laracuente

Research output: Contribution to journalArticlepeer-review


Trace inequalities are general techniques with many applications in quantum information theory, often replacing the classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivates entropy inequalities in type III von Neumann algebras that lack a semifinite trace. The Haagerup and Kosaki Lp spaces enable re-expressing trace inequalities in non-tracial von Neumann algebras. In particular, we show this for the generalized Araki-Lieb-Thirring and Golden-Thompson inequalities from the work of Sutter et al. [Commun. Math. Phys. 352(1), 37 (2017)]. Then, using the Haagerup approximation method, we prove a general von Neumann algebra version of universal recovery map corrections to the data processing inequality for relative entropy. We also show subharmonicity of a logarithmic p-fidelity of recovery. Furthermore, we prove that the non-decrease of relative entropy is equivalent to the existence of an L1-isometry implementing the channel on both input states.

Original languageEnglish (US)
Article number122204
JournalJournal of Mathematical Physics
Issue number12
StatePublished - Dec 1 2022

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Multivariate trace inequalities, p-fidelity, and universal recovery beyond tracial settings'. Together they form a unique fingerprint.

Cite this