Non-Markovianity of Gaussian channels

Torre, G. and Roga, W. and Illuminati, F. (2015) Non-Markovianity of Gaussian channels. Physical Review Letters, 115 (7). 070401. ISSN 1079-7114 (

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We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.