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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2018, Volume 151, Pages 117–125 (Mi into345)  

Tensor Products of Quantum Mappings

S. N. Filippov

Moscow Institute of Physics and Technology (State University)

Abstract: In this paper, we examine properties of the tensor powers of quantum mappings $\Phi$. In particular, we review positivity properties of unitary and non-unitary qubit mappings $\Phi^{\otimes 2}$. For arbitrary finite-dimensional systems, we present the relationship between the positive and completely positive divisibility of dynamical mappings $\Phi_t^{\otimes 2}$ and $\Phi_t$. A criterion of annihilation of entanglement by an arbitrary qubit mapping $\Phi^{\otimes 2}$ is found.

Keywords: quantum channel, complete positiveness, positive mapping, divisibility, tensor product

Funding Agency Grant Number
Russian Science Foundation 16-11-00084
This work was supported by the Russian Science Foundation (project No. 16-11-00084).


Full text: PDF file (214 kB)
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Bibliographic databases:

Document Type: Article
UDC: 519.72, 530.145
MSC: 15A69, 46L06

Citation: S. N. Filippov, “Tensor Products of Quantum Mappings”, Quantum probability, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 151, VINITI, Moscow, 2018, 117–125

Citation in format AMSBIB
\Bibitem{Fil18}
\by S.~N.~Filippov
\paper Tensor Products of Quantum Mappings
\inbook Quantum probability
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 151
\pages 117--125
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into345}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3903371}


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