2 problems

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Active common randomness outside the no-signaling polytope
Active-common-randomness conjecture. If $P(X,Y\mid A,B)$ has the displayed active-common-randomness factorization and $P(X,Y\mid A,B)\notin\mathscr{L}$ , then…
Conjecturerefutedcommon-randomness information-theory no-signalingarXiv posted 2 days ago
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Anantharam and Borkar's passive common randomness conjecture
Anantharam and Borkar's conjecture. Every point in $\mathscr{NS}$ is achievable through passive common randomness; equivalently, for any strategy $P(X,Y\mid A,B)$ satisfying the no…
Conjecturerefutedcommon-randomness information-theory no-signalingarXiv posted 2 days ago

Active common randomness outside the no-signaling polytope