Accounting for gauge symmetries in CHSH experiments

TL;DR

This work reexamines the CHSH scenario through the lens of gauge symmetries, showing that spontaneous breaking of rotational symmetry can enhance correlations and even produce CHSH violations in a local, deterministic framework. It introduces a statistical model with gauge degrees of freedom that preserves average symmetry yet allows a geometric phase to emerge from sequences of detector rotations, thereby relaxing the premises of the CHSH inequality. The authors argue that nature may select quantum-like correlations via information-theoretic criteria, notably a constant Fisher information for the quantum density, linking to minimum Fisher information principles and potentially to the Tsirelson bound. The paper also draws conceptual parallels to general relativity's gauge structure and outlines extensions to higher-dimensional and two-sphere settings for future work. Overall, it provides a physically intuitive, symmetry-based perspective on quantum correlations beyond standard quantum-only explanations.

Abstract

We re-examine the CHSH experiment, which we abstract here as a multi-round game played between two parties with each party reporting a single binary outcome at each round. We explore in particular the role that symmetries, and the spontaneous breaking thereof, play in determining the maximally achievable correlations between the two parties. We show, with the help of an explicit statistical model, that the spontaneous breaking of rotational symmetry allows for stronger correlations than those that can be achieved in its absence. We then demonstrate that spontaneous symmetry breaking may lead to a violation of the renowned CHSH inequality. We believe that the ideas presented in this paper open the door to novel research avenues that have the potential to deepen our understanding of the quantum formalism and the physical reality that it describes.

Figures (2)

• Figure 1: The basic assertion of the CHSH inequality. The CHSH inequality is based on the assertion that one can assign definite values to the four binary random variables $S_{A_1}, S_{A_2}, S_{B_1}$ and $S_{B_2}$ for any event in $\Omega$. The table illustrates four such events.
• Figure 2: A typical output table in a CHSH experiment. In each round of the game one and only one experimental setting is tested, $({\bm a}_i, {\bm b}_j)$ for $i,j\in\{1,2\}$ and the corresponding binary outputs, $S_{A_i}$ and $S_{B_j}$, are recorded. Unlike the table assumed in order to prove the CHSH theorem, cf. Fig. \ref{['fig:ineq_table']} in which all four columns are (or can be) filled out at each round, in the table obtained in a CHSH experiment only two columns are populated at each round.