Equivalence between face nonsignaling correlations, full nonlocality, all-versus-nothing proofs, and pseudotelepathy

We show that a quantum correlation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>p</a:mi></a:math> is in a face of the nonsignaling polytope with no local points if and only if <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>p</b:mi></b:math> has nonlocal content 1, if and only if <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>p</c:mi></c:math> allows for a Greenberger-Horne-Zeilinger-like proof, and if and only if <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>p</d:mi></d:math> provides a perfect strategy for a nonlocal game. That is, face nonsignaling (FNS) correlations, full nonlocality (FN), all-versus-nothing (AVN) proofs, and pseudotelepathy (PT) are equivalent. This shows that different resources behind a wide variety of fundamental results are in fact the same resource. We demonstrate that quantum correlations with FNS = FN = AVN = PT do not need to maximally violate a tight Bell inequality. We introduce a method for identifying quantum FNS = FN = AVN = PT correlations and use it to prove quantum mechanics does not allow for FNS = FN = AVN = PT neither in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mo>(</e:mo><e:mn>3</e:mn><e:mo>,</e:mo><e:mn>3</e:mn><e:mo>;</e:mo><e:mn>3</e:mn><e:mo>,</e:mo><e:mn>2</e:mn><e:mo>)</e:mo></e:mrow></e:math> nor in the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mo>(</f:mo><f:mn>3</f:mn><f:mo>,</f:mo><f:mn>2</f:mn><f:mo>;</f:mo><f:mn>3</f:mn><f:mo>,</f:mo><f:mn>4</f:mn><f:mo>)</f:mo></f:mrow></f:math> Bell scenarios. This solves an open problem that, because of the FNS = FN = AVN = PT equivalence, has implications in several fields. Published by the American Physical Society 2024