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3

To be clear: You have a Hilbert space $\mathcal{H}_A\otimes\mathcal{H}_B\otimes\mathcal{H}_C$. The initial state is $\rho_\text{tot}(0)=\rho_A\otimes\rho_B\otimes\rho_C$. There is a Hamiltonian acting on the system of the form $H_{\text{tot}}=H_{AB}\otimes\mathbb{I}_C+\mathbb{I}_A\otimes H_{BC}$ Instead of directly calculating the effect of the Hamiltonian ...

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I know this isn't really what you're thinking of with your question, but measurement-based quantum computing is pretty well studied. Under the many-worlds interpretation, the system counts as open for that protocol, because every time you perform a measurement you're becoming entangled with the system.

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That is a very old paper, corresponding to version one of the software. It is now on version 4.x. It is best to see the current documentation for how to use the Bloch sphere: http://qutip.org/docs/latest/guide/guide-bloch.html

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There are two possible answers. Let's say the universe evolves from $t=0$ to $t_f$ then the unitary evolution $U$ from $0$ to $t_f$ induces a CP evolution on the subsystem. To see this, note that the composition of CP maps is CP. Now, the reduced (system) evolution is $Tr_E U\rho_s\otimes\rho_E U^\dagger$ which is a composition of the map \$\rho_s\...

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