Extremal distributions under approximate majorization

Michał Horodecki , Jonathan Oppenheim , Carlo Sparaciari

Abstract

Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we consider a notion of approximate majorization. For any distribution, and given a distance δ, we find the approximate distributions which majorize (are majorized by) all other distributions within the distance δ. We call these the steepest and flattest approximation. This enables one to compute how close one can get to a given target distribution under a process governed by majorization. We show that the flattest and steepest approximations preserve ordering under majorization. Furthermore, we give a notion of majorization distance. This has applications ranging from thermodynamics, entanglement theory, and economics.
Author Michał Horodecki (FMPI / ITPA)
Michał Horodecki,,
- Institute of Theoretical Physics and Astrophysics
, Jonathan Oppenheim
Jonathan Oppenheim,,
-
, Carlo Sparaciari
Carlo Sparaciari,,
-
Journal seriesJournal of Physics A-Mathematical and Theoretical, ISSN 1751-8113, (A 30 pkt)
Issue year2018
Vol51
No30
Pages1-16
Publication size in sheets0.75
Article number305301
Keywords in Englishmajorization, state optimisation, approximate transformations
ASJC Classification2610 Mathematical Physics; 2611 Modelling and Simulation; 2613 Statistics and Probability; 3100 General Physics and Astronomy; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1088/1751-8121/aac87c
URL https://doi.org/10.1088/1751-8121/aac87c
Languageen angielski
Score (nominal)30
Score sourcejournalList
ScoreMinisterial score = 30.0, 21-05-2020, ArticleFromJournal
Publication indicators WoS Citations = 4; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 0.919; WoS Impact Factor: 2018 = 2.11 (2) - 2018=1.866 (5)
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