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Quantum decoherence means that when a quantum system interacts with its environment, coherence is lost, which means that all the density matrix becomes diagonal after the interaction. I never understood why it is so, but I get a clue here:
https://en.wikipedia.org/wiki/Quantum_decoherence#Dirac_notation
It says in particular (where ##\epsilon_i## and ##\epsilon_j## are states of the environment after the interaction):
"Additionally, decoherence requires, by virtue of the large number of hidden degrees of freedom in the environment, that
"
But why does a "large number of hidden degrees of freedom in the environment" imply approximate orthogonality of the evironmental states?
Is there any mathematical theorem where this is rigorously formulated and proved?
https://en.wikipedia.org/wiki/Quantum_decoherence#Dirac_notation
It says in particular (where ##\epsilon_i## and ##\epsilon_j## are states of the environment after the interaction):
"Additionally, decoherence requires, by virtue of the large number of hidden degrees of freedom in the environment, that
But why does a "large number of hidden degrees of freedom in the environment" imply approximate orthogonality of the evironmental states?
Is there any mathematical theorem where this is rigorously formulated and proved?
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