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Decoherence leads to an almost diagonalization of the density matrix of a quantum system (in a certain basis) after an uncontrolled interaction with the environment. How does the quantum system evolve after that? Does its state continue to change probabilistically, or deterministically in relation to the environment?

Арман Гаспарян
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I recommend to write down the density matrix of two entagled qubits (or spin up spin down states if you like). Then perform a measurement one one of the two qubits and see what density matrix you get (partial trace). It will be a mixed state. That's all. Simply put : decoherence is a what happens to a system of entangled states when only a sub part of the system (eg. one state) interacts with something. This something can but does not have to be an "uncontrolled interaction with the envionment". After that? The mixed state is a random ensemble of unentangled states that have not lost their non-determinism whatsoever. See also this post.

Kurt G.
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  • Thanks for the answer. And if one particle is measured, this is also decoherence. Then with what "part" of the system does the interaction take place? – Арман Гаспарян Feb 23 '22 at 20:14
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    Perhaps you mean the view that any measurement (even of just one particle) makes the apparatus entangled with the system (particle). On top of that composite system one could apply interaction with an environment to get decoherence. The best source that I know which is discussing this is the article by E. Joos about Decoherence in the book Entangled World by Audretsch et al. – Kurt G. Feb 23 '22 at 20:29