u/RecognitionAfter3485

Hey everyone, I've been digging into David Oaknin's paper "Accounting for gauge symmetries in CHSH experiments" (arXiv:2403.07935) and wanted to get a quick sanity check from the quantum info / black-box foundations crowd here.

In his model, he uses non-linear coordinate transformations (Gamma-maps) to ensure that the individual marginals are strictly setting-independent and non-signaling. However, the catch is that it forces the joint distribution of the hidden variables to depend explicitly on the relative detector angle, theta.

Oaknin argues this isn't a violation of locality or measurement independence because the hidden variables are purely relational (gauge-dependent) rather than absolute, which creates a geometric holonomy that breaks Counterfactual Definiteness instead.

From a quantum information / black-box perspective, how is this generally viewed by the community? Is this considered a genuine geometric bypass of Bell's theorem, or does having a joint distribution that depends on theta just relegate the whole model to a standard measurement-dependence / superdeterminism loophole?

I've been thinking about Bell's theorem and got confused about something..

Suppose a source emits particle pairs and each particle carries a hidden variable. So i can denote Alice's effective hidden variable as λ_A (which may depend on Alice's setting a) and Bob's as λ_B (which may depend on Bob's setting b).

Now suppose the following is true
1.The marginal distribution of λ_A alone does not depend on the settings a or b.
2.The marginal distribution of λ_B alone does not depend on the settings a or b.
3.But the joint distribution P(λ_A, λ_B) does depend on both settings through their relative angle θ = θ(a, b).

Now my question is -
Does such a model satisfy Bell's locality condition? Or does Bell's theorem require that the joint distribution P(λ_A, λ_B) also be independent of the measurement settings?

Intuitively I suspect this violates locality because Alice's outcome ultimately depends on Bob's setting through the joint structure — but I want to understand this precisely in terms of Bell's factorization condition.