Geodesic
Schmidt Number and Partially Entanglement-Breaking Channels in Infinite-Dimensional Quantum Systems
Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 775-789

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The Schmidt number of a state of an infinite-dimensional composite quantum system is defined and several properties of the corresponding Schmidt classes are considered. It is shown that there are states with given Schmidt number such that any of their countable convex decompositions does not contain pure states of finite Schmidt rank. The classes of infinite-dimensional partially entanglement-breaking channels are considered, and generalizations of several properties of such channels, which were obtained earlier in the finite-dimensional case, are proved. At the same time, it is shown that there are partially entanglement-breaking channels (in particular, entanglement-breaking channels) such that all of their operators in any Kraus representation are of infinite rank.
Keywords: Schmidt number, Schmidt rank, composite quantum system, quantum channel, Schmidt decomposition, partially entanglement-breaking channels.
Mots-clés : entanglement 
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     author = {M. E. Shirokov},
     title = {Schmidt {Number} and {Partially} {Entanglement-Breaking} {Channels} in {Infinite-Dimensional} {Quantum} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {775--789},
     publisher = {mathdoc},
     volume = {93},
     number = {5},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a12/}
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M. E. Shirokov. Schmidt Number and Partially Entanglement-Breaking Channels in Infinite-Dimensional Quantum Systems. Matematičeskie zametki, Tome 93 (2013) no. 5, pp. 775-789. http://geodesic.mathdoc.fr/item/MZM_2013_93_5_a12/