Markov triplets on CCR-algebras

Acta Scientiarum Mathematicarum

Volumn 76, Issue 1-2, 2010, Pages 111-134

  Jenčová, Anna ^a   Petz, Dénes ^b,c   Pitrik, József ^b  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

^b BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^c ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

Author keywords

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

Indexed keywords

EID: 77957220842     PISSN: 00016969     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (20)

1. L. ACCARDI, The space of square roots of measures and noncommutative Markov chains, Thesis, Moscow University, Faculty of Mathematics and Mechanics, 1973.
2. L. ACCARDI, On the noncommutative Markov property, Funkcional. Anal. i Prilozen., 9 (1975), 1-8 (in Russian).
3. L. ACCARDI, Some trends and problems in quantum probability, Quantum probability and applications to the quantum theory of irreversible processes, Lecture Notes in Math. 1055, Springer, 1984, 1-19.
4. L. ACCARDI and A. FRIGERIO, Markovian cocycles, Proc. R. Ir. Acad., 83 (1983), 251-263.
5. T. ANDO and D. PETZ, Gaussian Markov triplets approached by block matrices, Acta Sci. Math. (Szeged), 75 (2009), 329-345.
6. J. BLANK, P. EXNER and M. HAVLÍČEK, Hilbert space operators in quantum physics, American Institute of Physics, New York, 1994.
7. O. BRATTELI and D. W. ROBINSON, Operator algebras and quantum statistical mechanics I-II, Springer, 1979, 1981.
8. A. VAN DAELE and A. VERBEURE, Unitary equivalence of Fock representations on the Weyl algebra, Comm. Math. Phys., 20 (1971), 268-278.
9. P. HAYDEN, R. JÓZSA, D. PETZ and A. WINTER, Structure of states which satisfy strong subadditivity of quantum entropy with equality, Comm. Math. Phys., 246 (2004), 359-374.
10. A. S. HOLEVO, Probabilistic and statistical aspects of quantum theory, North-Holland, 1982.
11. R. HORN and CH. JOHNSON, Matrix Analysis, Cambridge Univ. Press, 1985.
12. A. JENČOVÁ and D. PETZ, Sufficiency in quantum statistical inference, Comm. Math. Phys., 263 (2006), 259-276.
13. E. H. LIEB and M. B. RUSKAI, Proof of the strong subadditivity of quantummechanical entropy, J. Math. Phys., 14 (1973), 1938-1941.
14. F. MANUCEAU and A. VERBEURE, Quasi-free states of the C. C. R.-algebra and Bogoliubov transformations, Comm. Math. Phys., 9 (1968), 293-302.
15. M. OHYA and D. PETZ, Quantum entropy and its use, Springer-Verlag, Heidelberg, 1993.
16. D. PETZ, An invitation to the algebra of the canonical commutation relation, Leuven University Press, Leuven, 1990.
17. D. PETZ, Entropy, the central limit theorem and the algebra of the canonical commutation relation, Lett. Math. Phys., 24 (1992), 211-220.
18. D. PETZ, Entropy of Markov states, Riv. di Math. Pura ed Appl., 14 (1994), 33-42.
19. D. PETZ, Quantum information theory and quantum statistics, Springer-Verlag, Heidelberg, 2008.
20. J. PITRIK, Markovian quasifree states on canonical anticommutation relation algebras, J. Math. Phys., 48 (2007), 112110.