A No-Go Theorem for Nonlocal Jamming from Analytic and Twistor Geometry

We investigate the possibility of nonlocal “jamming” of quantum correlations under relativistic causality constraints, in the sense of Grunhaus–Popescu–Rohrlich (GPR). Within the framework of quantum field theory, we model jamming as a modification of correlation functions and introduce a class of causally localized jammers, defined by a spacetime support condition together with a spectral condition. Under these assumptions, we prove an analytic no-go theorem: any such modification compatible with the analytic structure of QFT must vanish identically. The proof relies on the interplay between spacetime support and spectral support of distributions, highlighting a rigidity phenomenon analogous to Paley–Wiener type results. While a fully rigorous proof of the underlying spectral-support incompatibility lemma is deferred, the framework identifies a clear mathematical mechanism obstructing localized modifications of correlations. We further propose a geometric interpretation in twistor space. The analytic rigidity suggests a corresponding constraint on cohomology classes with restricted support. This leads to a precise conjecture formulated in terms of sheaf cohomology and long exact sequences, and connected to partial vanishing problems in the sense of Andreotti–Grauert. The relation with the Penrose transform is discussed at a heuristic level. The result establishes a structural obstruction to a broad class of causally localized jamming mechanisms and identifies a well-posed open problem at the interface of quantum field theory, complex geometry, and twistor theory.