Validity and failure of some entropy inequalities for CAR systems
Mathematical Physics
2009-11-10 v3 math.MP
Quantum Physics
Abstract
Basic properties of von Neumann entropy such as the triangle inequality and what we call MONO-SSA are studied for CAR systems. We show that both inequalities hold for any even state. We construct a certain class of noneven states giving counter examples of those inequalities. It is not always possible to extend a set of prepared states on disjoint regions to some joint state on the whole region for CAR systems. However, for every even state, we have its `symmetric purification' by which the validity of those inequalities is shown. Some (realized) noneven states have peculiar state correlations among subsystems and induce the failure of those inequalities.
Keywords
Cite
@article{arxiv.math-ph/0405042,
title = {Validity and failure of some entropy inequalities for CAR systems},
author = {Hajime Moriya},
journal= {arXiv preprint arXiv:math-ph/0405042},
year = {2009}
}
Comments
14 pages, latex, to appear in JMP. Some typos are corrected