### 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 language | English |
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Pages (from-to) | 111-134 |

Number of pages | 24 |

Journal | Acta Scientiarum Mathematicarum |

Volume | 76 |

Issue number | 1-2 |

Publication status | Published - 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.