Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 138, Pages 125–131 (Mi into218)  
Lower estimates for distances from a given quantum channel to certain classes of quantum channels

M. E. Shirokova, A. V. Bulinskib

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Full-text PDF (190 kB) English version article
Abstract: By using estimates for the variation of quantum mutual information and the relative entropy of entanglement, we obtain $\varepsilon$-exact lower estimates for distances from a given quantum channels to sets of degraded, anti-degraded, and entanglement-breaking channels. As an auxiliary result, we obtain $\varepsilon$-exact lower estimates for the distance from a given two-particle state to the set of all separable states.
Keywords: quantum state, quantum channel, coherent information, separable states, relative entropy of entanglement.
Funding agency Grant number
Russian Science Foundation 14-21-00162
The work of M. E. Shirokov was supported by the Russian Science Foundation (project No. 14-21-00162).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 2, Pages 237–244
DOI: https://doi.org/10.1007/s10958-019-04419-2
Bibliographic databases:
Document Type: Article
UDC: 519.248.3
MSC: 81P45, 94A40
Language: Russian
Citation: M. E. Shirokov, A. V. Bulinski, “Lower estimates for distances from a given quantum channel to certain classes of quantum channels”, Quantum computing, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 125–131; Journal of Mathematical Sciences, 241:2 (2019), 237–244
Citation in format AMSBIB
\Bibitem{ShiBul17}
\by M.~E.~Shirokov, A.~V.~Bulinski
\paper Lower estimates for distances from a given quantum channel to certain classes of quantum channels
\inbook Quantum computing
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 138
\pages 125--131
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into218}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3801255}
\zmath{https://zbmath.org/?q=an:1426.81019}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 2
\pages 237--244
\crossref{https://doi.org/10.1007/s10958-019-04419-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85069895421}
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