The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a maximally entangled configuration, preserve its entanglement even when applied an arbitrary number of times. In other words, a quantum channel ψ is said to be ES if its powers ψn are not entanglement-breaking for all integers n. We also characterize the properties of the Asymptotic Entanglement Saving (AES) maps. These form a proper subset of the ES channels that is constituted by those maps that not only preserve entanglement for all finite n but which also sustain an explicitly not null level of entanglement in the asymptotic limit n → ∞. Structure theorems are provided for ES and for AES maps which yield an almost complete characterization of the former and a full characterization of the latter.
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March 2016
Research Article|
March 02 2016
Entanglement-saving channels
L. Lami
;
L. Lami
1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física,
Universitat Autònoma de Barcelona
, 08193 Bellaterra, Barcelona, Spain
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V. Giovannetti
V. Giovannetti
2
NEST, Scuola Normale Superiore and Istituto Nanoscienze–CNR
, I-56127 Pisa, Italy
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J. Math. Phys. 57, 032201 (2016)
Article history
Received:
October 18 2015
Accepted:
February 09 2016
Citation
L. Lami, V. Giovannetti; Entanglement-saving channels. J. Math. Phys. 1 March 2016; 57 (3): 032201. https://doi.org/10.1063/1.4942495
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