| Summary: | 碩士 === 國立成功大學 === 物理學系 === 105 === According to Bell’s theorem, quantum systems exhibit stronger correlations than classical systems described by LHV (local hidden variables). In standard Bell scenarios,
the LHV is shared between all observers. In quantum networks however, resources have a distribution restricted according to a specific topology; the resulting local and quantum sets are particularly difficult to characterize. We consider the
simplest cyclic quantum network, the triangle, where the parties have only binary outputs. For the corresponding 3-local set, outer approximations are available using nonlinear inequalities, in particular the ones obtained by the inflation method (Wolfe et al.). On the other hand, only a few remarkable points are known to be 3-local. Thus, the status of a large part of the correlation space is unknown. We devise a method to find additional 3-local points to fill this unknown area, thus providing an inner approximation. We compare all these results by providing 2D and 3D visualizations of the subspace of symmetric correlations. Another open question is the existence of 3-quantum correlations that are not 3-local. We work in that direction
by producing random and structured 3-quantum distributions, and identifying the most promising candidates.
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