{
"id": "1912.00983",
"version": "v1",
"published": "2019-12-02T18:23:10.000Z",
"updated": "2019-12-02T18:23:10.000Z",
"title": "Adjusted Subadditivity of Relative Entropy for Non-commuting Conditional Expectations",
"authors": [
"Nicholas LaRacuente"
],
"comment": "15 pages, 1 figure",
"categories": [
"quant-ph",
"cs.IT",
"math.IT"
],
"abstract": "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.",
"revisions": [
{
"version": "v1",
"updated": "2019-12-02T18:23:10.000Z"
}
],
"analyses": {
"keywords": [
"non-commuting conditional expectations",
"adjusted subadditivity",
"trivial intersection",
"derive relative entropy decay estimates",
"von neumann subalgebras"
],
"note": {
"typesetting": "TeX",
"pages": 15,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}