Validity and failure of some entropy inequalities for CAR systems

Details Validity and failure of some entropy inequalities for CAR systems Validity and failure of some entropy inequalities for CAR systems

2004-05-14

arxiv.org/abs/math-ph/0405042v3

J. Math. Phys. 46. 033508 (2005)

Physics

Mathematical Physics

14 pages, latex, to appear in JMP. Some typos are corrected

Scientific paper

10.1063/1.1850995

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.

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