Markov triplets on CCR-algebras

Anna Jenčová, Dénes Petz, József Pitrik

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is defined by constant entropy increase. The Markov property of a quasifree state is described by the representing block matrix. The proof is based on results on the statistical sufficiency in the non-commutative case. The relation to classical Gaussian Markov triplets is also described. All rights reserved

Original languageEnglish
Pages (from-to)111-134
Number of pages24
JournalActa Scientiarum Mathematicarum
Volume76
Issue number1-2
Publication statusPublished - Oct 5 2010

Keywords

  • CCR algebra
  • Fock representation
  • Markov triplet
  • Quasi-free state
  • Von Neumann entropy
  • Weyl unitaries

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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  • Cite this

    Jenčová, A., Petz, D., & Pitrik, J. (2010). Markov triplets on CCR-algebras. Acta Scientiarum Mathematicarum, 76(1-2), 111-134.