Validity and failure of some entropy inequalities for CAR systems

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.

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

References in corpus (2)

• Equilibrium Statistical Mechanics of Fermion Lattice Systems
• Joint Extension of States of Subsystems for a CAR System

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