Horodecki, M;
Oppenheim, J;
Sparaciari, C;
(2018)
Extremal distributions under approximate majorization.
Journal of Physics A: Mathematical and Theoretical
, 51
(30)
, Article 305301. 10.1088/1751-8121/aac87c.
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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.
| Type: | Article |
|---|---|
| Title: | Extremal distributions under approximate majorization |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1751-8121/aac87c |
| Publisher version: | https://doi.org/10.1088/1751-8121/aac87c |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | majorization, state optimisation, approximate transformations |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Physics and Astronomy |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10085857 |
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