1. Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems. Oxford University Press, Oxford (2002)
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3. Kraus, K.: States, Effects, and Operations. Springer, Berlin (1983)
4. As a reminder, if $${\cal H}$$ and $${\cal K}$$ are Hilbert spaces, $${\cal R}\subset {\cal B}({\cal H})$$ is a $${\mathbb{C}}$$-linear subspace spanned by states, and $$F:{\cal R}\rightarrow {\cal B}({\cal K})$$ is $${\mathbb{C}}$$-linear, then $$F$$ is completely positive if $$F\otimes \text{ id } :{\cal R}\otimes {\cal B}({\cal H}_{\text{ W }}) \rightarrow {\cal B}({\cal K})\otimes {\cal B}({\cal H}_{\text{ W }})$$ is a positive map for all finite dimensional $${\cal H}_{\text{ W }}$$
5. Rodríguez-Rosario, C.A., Modi, K., Kuah, A., Shaji, A., Sudarshan, E.C.G.: Completely positive maps and classical correlations. J. Phys. A 41(20), 205301 (2008)