The Choi-Jamiolkowski forms of quantum Gaussian channels

We obtain explicit expressions for the Choi-Jamiolkowski (CJ) forms and operators defining a general bosonic Gaussian channel. The four principal cases are considered in Sec. III; in Sec. IV, we give a decomposition of Gaussian CJ form into product of these four principal types and provide a necessary and sufficient condition for the existence of the bounded CJ operator. (C) 2011 American Institute of Physics. [doi:10.1063/1.3581879]