Visualization the set of 3-local and 3-quantum correlation

  • 尤 瑞揚

Student thesis: Master's Thesis

Abstract

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
Date of Award2017 Jan 23
Original languageEnglish
SupervisorYeong-Cherng Liang (Supervisor)

Cite this

'