# CONFLUENTES MATHEMATICI

Ergodic Dilation of a Quantum Dynamical System
Confluentes Mathematici, Tome 6 (2014) no. 1, pp. 77-93.

Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.

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DOI : https://doi.org/10.5802/cml.14
Classification : 46L07,  46L55,  46L57
Mots clés : Quantum Markov process, completely positive maps, Nagy dilation, ergodic state.
@article{CML_2014__6_1_77_0,
author = {Carlo Pandiscia},
title = {Ergodic {Dilation} of a {Quantum} {Dynamical} {System}},
journal = {Confluentes Mathematici},
pages = {77--93},
publisher = {Institut Camille Jordan},
volume = {6},
number = {1},
year = {2014},
doi = {10.5802/cml.14},
mrnumber = {3266886},
zbl = {1323.46045},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.14/}
}
Carlo Pandiscia. Ergodic Dilation of a Quantum Dynamical System. Confluentes Mathematici, Tome 6 (2014) no. 1, pp. 77-93. doi : 10.5802/cml.14. https://cml.centre-mersenne.org/articles/10.5802/cml.14/

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