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Many body quantum states analyzed as probabilistic sequences

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Measurements of consecutive sites in a many body qudit system (e.q. a spin chain) can be interpreted as generating a probabilistic sequence of numbers $X_1 X_2 X_3 \ldots$, where $X_i\in \{0,1,\ldots,d-1 \}$.

Are there any studies on that approach, in particular - exploring predictability of such systems or constructing a Markov model of some order simulating it?

This post has been migrated from (A51.SE)
asked Jan 25, 2012 in Theoretical Physics by Piotr Migdal (1,250 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
Maybe I'm missing something (I'm about to go to sleep). You take the spin-spin correlation functions and build (say) whatever order transition matrix you like, no?

This post has been migrated from (A51.SE)
@SHuntsman In the one ways (state -> sequence) it is straightforward. I am interested what can one deduce about the state (or Hamiltonian, if it an ground/eigenstate) knowing only the sequence.

This post has been migrated from (A51.SE)

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