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I am currently reading about Tsirelson's problem, and have a few questions. I hope you can give me your pardon, if they seem ill-posed or misinformed,

Here is what I understand so far--or at least I think I understand! Tsirelson's problem seems to be about whether two mathematicals models yield the same correlation functions. The physical situation being modelled is that of two independent observers (Alice and Bob) conducting measurements on the same physical system, which is commonly modelled using a tensor product of Hilbert spaces, each factor corresponding to an observer conducting measurements on a physical system being measured. The other model used is some bigger Hilbert space and the assumption that all the observables of Alice commute with all of Bob's.

My first question is, how equivalent are these two models, irrespective of whether they yield the same correlation functions? It would seem that they have to agree in some respects otherwise we would reject one model as incorrect.

My next question is, what if the system consists of entangled particles, or does "independent observers" exclude this possibility? If there is no entanglement, why wouldn't the two observers measure the same things? If they did make the same exact measurements, would that imply they have the same Hilbert spaces...yes? no?

Again, please be gracious of my ignorance. I would really like to understand this problem. Thank you!

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# Tsirelson's Problem

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