Extreme points of the set of quantum states with bounded energy
Quantum Physics
2021-09-28 v1 Mathematical Physics
Functional Analysis
math.MP
Abstract
We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. This allows us to write every state with bounded energy in terms of a continuous convex combination of pure states of bounded energy. Furthermore, we prove that any quantum state with finite energy can be represented as a continuous convex combination of pure states with the same energy. We discuss examples from quantum information theory.
Keywords
Cite
@article{arxiv.2002.03969,
title = {Extreme points of the set of quantum states with bounded energy},
author = {Stephan Weis and Maksim Shirokov},
journal= {arXiv preprint arXiv:2002.03969},
year = {2021}
}
Comments
Preliminary version. Any comments and references are welcome