hyperlinear

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 hyperlinear [2020/08/28 15:52] – admin hyperlinear [2020/08/28 15:54] (current) – admin Both sides previous revisionPrevious revision2020/08/28 15:54 admin 2020/08/28 15:52 admin 2020/08/28 15:50 admin created 2020/08/28 15:54 admin 2020/08/28 15:52 admin 2020/08/28 15:50 admin created Line 3: Line 3: A positive resolution to Connes' embedding problem would've [[https://arxiv.org/pdf/1309.2034.pdf|implied]] that all countable discrete groups are hyperlinear. Since MIP*=RE gives a negative answer to CEP, this leaves open the possibility that there are non-hyperlinear groups. A positive resolution to Connes' embedding problem would've [[https://arxiv.org/pdf/1309.2034.pdf|implied]] that all countable discrete groups are hyperlinear. Since MIP*=RE gives a negative answer to CEP, this leaves open the possibility that there are non-hyperlinear groups. - One approach to this is to create a linear constraint system (LCS) game $G$ whose commuting operator value $\omega^{co}(G)$ is different from its tensor product value $\omega^*(G)$. + One [[https://simons.berkeley.edu/sites/default/files/docs/15568/williamslofstraslides-quantumprotocols.pdf|approach]] to this is to create a linear constraint system (LCS) game $G$ whose commuting operator value $\omega^{co}(G)$ is different from its tensor product value $\omega^*(G)$. + + Thus, can the separating nonlocal game constructed in the MIP*=RE paper be formulated as a linear constraint system game?