Tensor Products of Quantum Mappings

S. N. Filippov

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

Résumé

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.

Détail

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

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