A number of results connecting quantum and classical Markov semigroups, as well as their dilations is reported. The method presented here is based on the analysis of the structure of the semigroup generator. In particular, measure-valued processes appear as a combination of classical reduction and classical dilation of a given quantum Markov semigroup.
@article{CML_2009__1_1_123_0,
author = {Rolando Rebolledo},
title = {Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups},
journal = {Confluentes Mathematici},
pages = {123--167},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {1},
number = {1},
year = {2009},
doi = {10.1142/S1793744209000055},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.1142/S1793744209000055/}
}
TY - JOUR AU - Rolando Rebolledo TI - Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups JO - Confluentes Mathematici PY - 2009 SP - 123 EP - 167 VL - 1 IS - 1 PB - World Scientific Publishing Co Pte Ltd UR - https://cml.centre-mersenne.org/articles/10.1142/S1793744209000055/ DO - 10.1142/S1793744209000055 LA - en ID - CML_2009__1_1_123_0 ER -
%0 Journal Article %A Rolando Rebolledo %T Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups %J Confluentes Mathematici %D 2009 %P 123-167 %V 1 %N 1 %I World Scientific Publishing Co Pte Ltd %U https://cml.centre-mersenne.org/articles/10.1142/S1793744209000055/ %R 10.1142/S1793744209000055 %G en %F CML_2009__1_1_123_0
Rolando Rebolledo. Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups. Confluentes Mathematici, Tome 1 (2009) no. 1, pp. 123-167. doi : 10.1142/S1793744209000055. https://cml.centre-mersenne.org/articles/10.1142/S1793744209000055/
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