Ergodic Dilation of a Quantum Dynamical System
Confluentes Mathematici, Volume 6 (2014) no. 1, p. 77-91

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.

DOI : https://doi.org/10.5802/cml.14
Classification:  46L07,  46L55,  46L57
Keywords: Quantum Markov process, completely positive maps, Nagy dilation, ergodic state.
@article{CML_2014__6_1_77_0,
     author = {Pandiscia, Carlo},
     title = {Ergodic Dilation of a Quantum Dynamical System},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {6},
     number = {1},
     year = {2014},
     pages = {77-91},
     doi = {10.5802/cml.14},
     language = {en},
     url = {http://www.numdam.org/item/CML_2014__6_1_77_0}
}
Pandiscia, Carlo. Ergodic Dilation of a Quantum Dynamical System. Confluentes Mathematici, Volume 6 (2014) no. 1, pp. 77-91. doi : 10.5802/cml.14. http://www.numdam.org/item/CML_2014__6_1_77_0/

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