Geodesic
Entropy gain and the~Choi--Jamiolkowski correspondence for infinite-dimensional quantum evolutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 142-159

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We consider the entropy gain for infinite-dimensional evolutions and show that unlike in the finite-dimensional case, there are many channels with positive minimal entropy gain. We obtain a new lower bound and compute the minimal entropy gain for a broad class of bosonic Gaussian channels. We mathematically formulate the Choi–Jamiolkowski (CJ) correspondence between channels and states in the infinite-dimensional case in a form close to the form used in quantum information theory. In particular, we obtain an explicit expression for the CJ operator defining a general nondegenerate bosonic Gaussian channel and compute its norm.
Keywords: quantum entropy, completely positive map, Choi–Jamiolkowski correspondence, bosonic Gaussian channel. 
@article{TMF_2011_166_1_a9,
     author = {A. S. Holevo},
     title = {Entropy gain and {the~Choi--Jamiolkowski} correspondence for infinite-dimensional quantum evolutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {142--159},
     publisher = {mathdoc},
     volume = {166},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a9/}
}
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A. S. Holevo. Entropy gain and the~Choi--Jamiolkowski correspondence for infinite-dimensional quantum evolutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 142-159. http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a9/