Many body quantum states analyzed as probabilistic sequences

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?

• 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? Jan 28, 2012 at 3:23
• @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. Jan 28, 2012 at 10:12