### arXiv:1912.00983 [quant-ph]AbstractReferencesReviewsResources

#### Adjusted Subadditivity of Relative Entropy for Non-commuting Conditional Expectations

Published 2019-12-02Version 1

If a set of von Neumann subalgebras has a trivial intersection in finite dimension, then the sum of relative entropies of a given density to its projection in each such algebra is larger than a multiple of its relative entropy to its projection in the trivial intersection. This results in a subadditivity of relative entropy with a dimension and algebra-dependent, multiplicative constant. As a primary application, this inequality lets us derive relative entropy decay estimates in the form of modified logarithmic-Sobolev inequalities for complicated quantum Markov semigroups from those of simpler constituents.

**Comments:**15 pages, 1 figure