Validity and failure of some entropy inequalities for CAR systems | Zendy

Hajime Moriya | Zendy

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Validity and failure of some entropy inequalities for CAR systems

Author(s) -

Hajime Moriya

Publication year - 2005

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1850995

Subject(s) - disjoint sets , inequality , mathematics , entropy (arrow of time) , state (computer science) , von neumann entropy , von neumann architecture , class (philosophy) , pure mathematics , statistical physics , discrete mathematics , computer science , quantum entanglement , mathematical analysis , physics , quantum , quantum mechanics , algorithm , artificial intelligence

Basic properties of von Neumann entropy such as the triangle inequality andwhat we call MONO-SSA are studied for CAR systems. We show that both inequalities hold for any even state. We construct acertain class of noneven states giving counter examples of those inequalities. It is not always possible to extend a set of prepared states on disjointregions to some joint state on the whole region for CAR systems. However, for every even state, we have its `symmetric purification' by whichthe validity of those inequalities is shown. Some (realized) noneven states have peculiar state correlations amongsubsystems and induce the failure of those inequalities.Comment: 14 pages, latex, to appear in JMP. Some typos are correcte

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