Geodesic
Tensor Products of Quantum Mappings
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 117-125

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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. 
@article{INTO_2018_151_a10,
     author = {S. N. Filippov},
     title = {Tensor {Products} of {Quantum} {Mappings}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {117--125},
     publisher = {mathdoc},
     volume = {151},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_151_a10/}
}
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S. N. Filippov. Tensor Products of Quantum Mappings. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum probability, Tome 151 (2018), pp. 117-125. http://geodesic.mathdoc.fr/item/INTO_2018_151_a10/