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In Zurek's theory of quantum Darwinism, information about the pointer states of a system imprint themselves upon fragments of the environment carrying records about the state of the system. Multipartite entanglement between the system and the many fragments effectively become classical correlations whenever one doesn't have access to all the fragments due to the monogamy of entanglement.

So far, so good, but typically, the fragments are themselves in a superposition; a superposition of their locations, a superposition of the form of their encodings of their records, a superposition of existing and not existing, etc. This problem becomes especially acute whenever the density of record carrying fragments is very low, but still high enough to lead to decoherence. Even only two imprintings upon the environment are enough if the observer intercepts one of them while the other forever escapes him. Given this, how can one perform a proper quantum Darwinism analysis unless one already knew in advance where the record carrying fragments are and the form of their encoding? And to specify where the records are and how they are encoded, doesn't one have to resort to a decoherence analysis of the environment prior to that, and isn't that circular?

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I find it very hard to isolate the question you're asking or the hypothetical paradox or incompleteness that you seem to claim to have found. The environment is a "witness" to the state of the system, and what are the particular observables that it may see of course does depend on the dynamics, much like the outcome of Darwin's selection in biology does depend on the animals' eating of each other. The outcome isn't determined in advance. Well, one may guess the outcome in advance, but in that case, he obviously has to know as much as possible about the processes that will take place. –  LuboŇ° Motl Dec 28 '11 at 9:34
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