Relating Wigner's Friend Scenarios to Nonclassical Causal Compatibility, Monogamy Relations, and Fine Tuning

Nonclassical causal modeling was developed in order to explain violations of Bell inequalities while adhering to relativistic causal structure and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>f</mml:mi><mml:mi>a</mml:mi><mml:mi>i</mml:mi><mml:mi>t</mml:mi><mml:mi>h</mml:mi><mml:mi>f</mml:mi><mml:mi>u</mml:mi><mml:mi>l</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi></mml:math>---that is, avoiding fine-tuned causal explanations. Recently, a no-go theorem that can be viewed as being stronger than Bell's theorem has been derived, based on extensions of the Wigner's friend thought experiment: the Local Friendliness (LF) no-go theorem. Here we show that the LF no-go theorem poses formidable challenges for the field of causal modeling, even when nonclassical and/or cyclic causal explanations are considered. We first recast the LF inequalities, one of the key elements of the LF no-go theorem, as special cases of monogamy relations stemming from a statistical marginal problem. We then further recast LF inequalities as causal compatibility inequalities stemming from a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>s</mml:mi><mml:mi>s</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:math> causal marginal problem, for a causal structure implied by well-motivated causal-metaphysical assumptions. We find that the LF inequalities emerge from this causal structure even when one allows the latent causes of observed events to admit post-quantum descriptions, such as in a generalized probabilistic theory or in an even more exotic theory. We further prove that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>n</mml:mi><mml:mi>o</mml:mi></mml:math> nonclassical causal model can explain violations of LF inequalities without violating the No Fine-Tuning principle. Finally, we note that these obstacles cannot be overcome even if one appeals to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>c</mml:mi><mml:mi>y</mml:mi><mml:mi>c</mml:mi><mml:mi>l</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi></mml:math> causal models, and we discuss potential directions for further extensions of the causal modeling framework.