# Comparing quantum dynamical entropies

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 411-420
- ISSN: 0137-6934

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topTuyls, P.. "Comparing quantum dynamical entropies." Banach Center Publications 43.1 (1998): 411-420. <http://eudml.org/doc/208861>.

@article{Tuyls1998,

abstract = {Last years, the search for a good theory of quantum dynamical entropy has been very much intensified. This is not only due to its usefulness in quantum probability but mainly because it is a very promising tool for the theory of quantum chaos. Nowadays, there are several constructions which try to fulfill this need, some of which are more mathematically inspired such as CNT (Connes, Narnhofer, Thirring), and the one proposed by Voiculescu, others are more inspired by physics such as ALF (Alicki, Lindblad, Fannes). Therefore, a natural question arises whether there is a relation between all these different notions. In this paper we will indicate that the CNT entropy turns out to be smaller than the ALF dynamical entropy.},

author = {Tuyls, P.},

journal = {Banach Center Publications},

keywords = {quantum dynamical entropies; ALF dynamical entropy; CNT entropy; speed of information transmission; Holevo-Levitin inequality},

language = {eng},

number = {1},

pages = {411-420},

title = {Comparing quantum dynamical entropies},

url = {http://eudml.org/doc/208861},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Tuyls, P.

TI - Comparing quantum dynamical entropies

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 411

EP - 420

AB - Last years, the search for a good theory of quantum dynamical entropy has been very much intensified. This is not only due to its usefulness in quantum probability but mainly because it is a very promising tool for the theory of quantum chaos. Nowadays, there are several constructions which try to fulfill this need, some of which are more mathematically inspired such as CNT (Connes, Narnhofer, Thirring), and the one proposed by Voiculescu, others are more inspired by physics such as ALF (Alicki, Lindblad, Fannes). Therefore, a natural question arises whether there is a relation between all these different notions. In this paper we will indicate that the CNT entropy turns out to be smaller than the ALF dynamical entropy.

LA - eng

KW - quantum dynamical entropies; ALF dynamical entropy; CNT entropy; speed of information transmission; Holevo-Levitin inequality

UR - http://eudml.org/doc/208861

ER -

## References

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- [TUY] P. Tuyls, Towards Quantum Kolmogorov-Sinai entropy, Ph.D. thesis, 1997.

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