Abstract
Consider now the case where the total Hilbert space can be decomposed into two parts.
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Notes
- 1.
Leaving aside the case of factorized global dynamics \(U(t_1,t_0)=U_{A}(t_1,t_0)\otimes U_{B}(t_1,t_0),\) see: D. Salgado and J. L. Sánchez-Gómez, Comment on “Dynamics of open quantum systems initially entangled with environment: Beyond the Kraus representation” arXiv:quantph/0211164 (2002); H. Hayashi, G. Kimura, Y. Ota, Phs. Rev. A 67, 062109 (2003).
- 2.
Note that the composition of two completely positive maps is also a completely positive map. However the composition of two arbitrary operators can be completely positive regardless of whether they are individually completely positive or not
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Rivas, A., Huelga, S.F. (2012). Time Evolution in Open Quantum Systems. In: Open Quantum Systems. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23354-8_3
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DOI: https://doi.org/10.1007/978-3-642-23354-8_3
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