On distilling secure key from reducible private states and (non)existence of entangled key-undistillable states

Karol Horodecki , Piotr Ćwikliński , Adam Rutkowski , Michał Studziński

Abstract

Hereunder, we study the class of irreducible private states that are private states from which all the secret content is accessible via measuring their key part. We provide the first protocol which distills key not only from the key part, but also from the shield if only the state is reducible. We prove also a tighter upper bound on the performance of that protocol, given in terms of regularized relative entropy of entanglement instead of relative entropy of entanglement previously known. This implies in particular that the irreducible private states are all strictly irreducible if and only if the entangled but key-undistillable states ('entangled key-undistilable states') exist. In turn, all the irreducible private states of the dimension 4 ⨂ 4 are strictly irreducible, that is, after an attack on the key part they become separable. Provided the bound key states exist, we consider different subclasses of the irreducible private states and their properties. Finally we provide a lower bound on the trace norm distance between key-undistillable states and private states, in sufficiently high dimensions.
Author Karol Horodecki (FMPI / II)
Karol Horodecki,,
- Institute of Informatics
, Piotr Ćwikliński (FMPI / ITPA)
Piotr Ćwikliński,,
- Institute of Theoretical Physics and Astrophysics
, Adam Rutkowski (FMPI / ITPA)
Adam Rutkowski,,
- Institute of Theoretical Physics and Astrophysics
, Michał Studziński
Michał Studziński,,
-
Journal seriesNew Journal of Physics, ISSN , e-ISSN 1367-2630, (A 40 pkt)
Issue year2018
Vol20
Pages1-24
Publication size in sheets1.05
Keywords in Englishprivate states, irreducible private states, key distillation, bound key state
DOIDOI:10.1088/1367-2630/aad75a
URL http://iopscience.iop.org/article/10.1088/1367-2630/aad75a/pdf
Languageen angielski
LicenseJournal (articles only); published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)40
ScoreMinisterial score = 40.0, 09-10-2018, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 09-10-2018, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 3.786 (2) - 2016=3.637 (5)
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