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Usually in QFT, even optical quantum mechanics papers, usually resort to describe n-states in terms of the ladder algebra, plus a parameter for polarization, but the entanglement information is usually not presented in such a neat, definite way.

I was wondering if anyone has attempted to describe entanglement as a sort of Ladder-like, or finite algebra.

A problem that I might see with pursuing such approach is that is basically trying to 'dynamicise' the degrees of freedom of entanglement around a minima of potential where you can construct a lattice of k-states called phonons, or in this case, entanglons.

Since the motivation for the question is that I'm interested in all kind of weird ad-hoc, or mathematically motivated non-standard descriptions of quantum entanglement, feel free to add some other approaches you might know as an answer, even if they haven't been fruitful. I'll still upvote it if it is interesting

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  • $\begingroup$ What is your definition of "the entanglement information"? Also, what do you call "the Wick algebra"? (a google search is rather inconclusive) States of what are we looking at? What subsystems are combined here to have entangled states? $\endgroup$
    – ACuriousMind
    Commented Mar 28, 2015 at 22:10
  • $\begingroup$ sorry, I meant Ladder algebra, I corrected it on the question $\endgroup$
    – lurscher
    Commented Mar 28, 2015 at 23:15
  • $\begingroup$ entanglement information the way you describe your quantum correlations between the excitations $\endgroup$
    – lurscher
    Commented Mar 28, 2015 at 23:17
  • $\begingroup$ I was hoping for something more rigorous than "quantum correlations". Also, I don't see how QFT would see "entanglement information" as anything noteworthy at all - usually, entanglement arises in QM when combining individual systems into larger systems. But in QFT, you do not consider the individual particles to be QM systems in their own right anymore, they just live inside the larger Fock space, in which all "entangled" and "nonentangled" states equally lie. $\endgroup$
    – ACuriousMind
    Commented Mar 28, 2015 at 23:27
  • $\begingroup$ entanglement is no interaction. It's merely statistical correlation. That is, one cannot formulate a potential for it. If there is some information one can obtain about a subsytem by measurment on a different subsystem, this is only due to conversation laws or some premise that hold anyway. $\endgroup$
    – image357
    Commented Mar 28, 2015 at 23:27

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No idea if applying Fock algebras to the entanglement description would lead to anything "fruitful", I haven't seen any of that.

What I've seen is the emergence of Tensor Network Methods in order to describe entanglement of many-body systems. There is the possibility that TNM can be related with holographic descriptions of gravity.

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