Papers › Graph-theoretic approach to Bell experiments with low detection efficiency
Graph-theoretic approach to Bell experiments with low detection efficiency
Zhen-Peng Xu, Jonathan Steinberg, Jaskaran Singh, Antonio J. López-Tarrida, José R. Portillo, Adán Cabello
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Bell inequality tests where the detection efficiency is below a certain threshold η_(crit) can be simulated with local hidden-variable models. Here, we introduce a method to identify Bell tests requiring low η_(crit) and relatively low dimension d of the local quantum systems. The method has two steps. First, we show a family of bipartite Bell inequalities for which, for correlations produced by maximally entangled states, η_(crit) can be upper bounded by a function of some invariants of graphs, and use it to identify correlations that require small η_(crit). We present examples in which, for maximally entangled states, η_(crit) ≤0.516 for d=16, η_(crit) ≤0.407 for d=28, and η_(crit) ≤0.326 for d=32. We also show evidence that the upper bound for η_(crit) can be lowered down to $0.415$ for d=16 and present a method to make the upper bound of η_(crit) arbitrarily small by increasing the dimension and the number of settings. All these upper bounds for η_(crit) are valid (as it is the case in the literature) assuming no noise. The second step is based on the observation that, using the initial state and measurement settings identified in the first step, we can construct Bell inequalities with smaller η_(crit) and better noise robustness. For that, we use a modified version of Gilbert's algorithm that takes advantage of the automorphisms of the graphs used in the first step. We illustrate its power by explicitly developing an example in which η_(crit) is 12.38% lower and the required visibility is 14.62% lower than the upper bounds obtained in the first step. The tools presented here may allow for developing high-dimensional loophole-free Bell tests and loophole-free Bell nonlocality over long distances.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections