I have seen it written that after a preferred basis (for example |1>, |2>) is chosen a pure state say(adsbygoogle = window.adsbygoogle || []).push({});

[c^2]|1><1|+[(1-c)^2]|2><2|+c(1-c)|1><2|+c(1-c)|2><1| will reduce to the mixed state

c^2|1><1|+(1-c)^2|2><2|.

I wonder about the necessity of this "pre-reduction" postulate. It seems to me that rather than adding this postulate, we can say that once we have chosen what observable it is we are going to measure(and hence the preferred basis) that the information conveyed by the |1><2| and |2><1| terms are inaccessible because the only things that are accessible to us are the eigenstates(|1><1|, |2><2|).

I guess my question is could someone please explain to me what is the need to add this non-unitary pre-reduction of a pure state into a mixed state.

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# Preferred basis and prereduction of density matrices

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