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Gleason's theorem fails if the dimension of the Hilbert space is two. Does this allow for violations of Born's rule in two-dimensional systems? Or can you somehow tensor the system with the (ever-present and infinite-dimensional) Hilbert space of the rest of the universe, apply Gleason's theorem and reduce to the system again to find Born's rule in the original 2D system?

Have experiments been conducted to check for violations of Born's rule in 2D systems?

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# Possibility of violations of Born's rule in two dimensions?

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