Sufficient separability criteria and linear maps

Remigiusz Augusiak , Dariusz Chruściński , Maciej Lewenstein , Swapan Rana , Jan Samsonowicz


We study families of positive and completely positive maps acting on a bipartite system C^M⊗C^N (with M≤N). The maps have a property that, when applied to any state (of a given entanglement class), result in a separable state or, more generally, a state of another certain entanglement class (e.g., Schmidt number ≤k). This allows us to derive useful families of sufficient separability criteria. Explicit examples of such criteria have been constructed for arbitrary M,N, with a special emphasis on M=2. Our results can be viewed as generalizations of the known facts that in the sufficiently close vicinity of the completely depolarized state (the normalized identity matrix), all states are separable (belong to “weakly” entangled classes). Alternatively, some of our results can be viewed as an entanglement classification for a certain family of states, corresponding to mixtures of the completely polarized state with pure states, partial transposes, and/or local transformations thereof
Author Remigiusz Augusiak
Remigiusz Augusiak,,
, Dariusz Chruściński
Dariusz Chruściński,,
, Maciej Lewenstein
Maciej Lewenstein,,
, Swapan Rana
Swapan Rana,,
, Jan Samsonowicz ZGR
Jan Samsonowicz,,
- Department of Differential Geometry
Journal seriesPhysical Review A, ISSN 1050-2947 []
Issue year2016
Publication size in sheets0.3
Keywords in Englishquantum states, positive maps, entanglement, separability of states
Abstract in PolishBadane są rodziny dodatnich i całkowicie dodatnich odwzorowań stanów kwantowych (dodatnio określonych operatorów ustalonego wymiaru nxm przestrzeni Hilberta), w języku których konstruujemy warunki dostateczne do tego aby stan był separowalny (nie splątany). Udowodnione zostały uogólnienia niektórych znanych i pewnych nowych kryteriów separowalności i splątania.
Languageen angielski
Score (nominal)35
ScoreMinisterial score = 35.0, 28-11-2017, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 28-11-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2014 = 2.808 (2) - 2014=2.628 (5)
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