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Maximum-likelihood reconstruction of CP maps

Massimiliano F. Sacchi
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Abstract

We present a method for the determination of the completely positive (CP) map describing a physical device based on random preparation of the input states, random measurements at the output, and maximum-likelihood principle. In the numerical implementation the constraint of completely positivity can be imposed by exploiting the isomorphism between linear transformations from Hilbert spaces $\cal H$ to $\cal K$ and linear operators in ${\cal K}\otimes {\cal H}$. The effectiveness of the method is shown on the basis of some examples of reconstruction of CP maps related to quantum communication channels for qubits.

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Massimiliano F. Sacchi. 2000-09-26. Maximum-likelihood reconstruction of CP maps. https://doi.org/10.1103/physreva.63.054104

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