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

Eduardo Gonzalez-Granda Fernandez

Published Apr 23, 2026• 0 citations
Publisher

Abstract

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.This work motivates subsequent analytic and spectral results developed in DOI;10.5281/zenodo.19713348

DOI
10.5281/zenodo.19713347

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quant-pharXiv:2608.20247•Aug 21, 2026•0 citations
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.This work motivates subsequent analytic and spectral results developed in DOI;10.5281/zenodo.19713348
We prove a no-go theorem for nonlocal jamming mechanisms under the spectral condition of relativistic quantum field theory. Modeling the action of a jammer as a modification of correlation functions subject to causal localization, we show that any such modification compatible with positive energy must vanish identically. The proof is based on Fourier-analytic arguments and the structure of distributions with spectral support in the forward light cone. In particular, the result follows from the incompatibility between causal support in spacetime and spectral support in momentum space, which forces triviality under mild regularity assumptions. This establishes that nonlocal jamming is impossible within any framework that preserves the spectral condition and causal localization. The result is independent of detailed analytic properties beyond those implied by positive energy. We also discuss a geometric interpretation of this obstruction in twistor space. In that setting, localized modifications correspond to cohomological data with restricted support, suggesting a form of global rigidity. This geometric formulation is presented as a conjectural extension and an open problem. The work connects foundational questions in quantum information (nonlocal correlations and jamming) with structural aspects of quantum field theory, highlighting the constraining role of spectral and analytic principles. This work is further developed in DOI: 10.5281/zenodo.19713348, where a classification of hidden-variable extensions is established.
This work investigates structural constraints imposed by analyticity in relativistic quantum field theory on classical causal explanations of quantum correlations. Building on previous results on analytic rigidity, we establish a conditional obstruction to the realization of classical causal factorizations through spacetime-localized modifications of two-point correlation functions. The argument derives analyticity directly from the spectral condition and identifies clustering as the key mechanism linking probabilistic factorization with analytic constraints. We then extend the analysis to three-point functions. A marginal spectral condition is introduced as a natural generalization compatible with dimensional reduction. Under this framework, we prove that any admissible modification must vanish upon reduction to all two-point marginals. The irreducible three-point sector is analyzed via connected correlation functions. A conditional obstruction is obtained under an extended analytic rigidity hypothesis in higher-dimensional tube domains, which is formulated explicitly as an open problem. The work provides a unified perspective connecting analytic properties of quantum field theory with causal modeling approaches to quantum correlations, and outlines a program for extending these results to higher-point functions.
This work investigates structural constraints on hidden-variable extensions of relativistic quantum field theory imposed by analyticity and the spectral condition. Building on a previously established no-go theorem for causally localized modifications, we analyze relativistic Bohmian quantum field theories, focusing on the multi-time framework developed by Hrvoje Nikolić. We show that any hidden-variable extension preserving Wightman analyticity cannot be represented as a localized spacetime modification of correlation functions. Instead, viable theories must abandon spacetime localization and exhibit intrinsically nonlocal structures defined on configuration space. This provides a structural explanation for the nonlocal character of Bohmian quantum field theories and clarifies the distinction between strong (distributional) localization and weak (operational) localization. The paper also proposes a classification of nonlocal hidden-variable models and explores connections with causal-model approaches to quantum correlations.
This work investigates the compatibility of hidden-variable modifications with the analytic structure of relativistic quantum field theory (QFT). Working within the framework of tempered distributions, we analyze three fundamental properties: the spectral condition, analyticity in the forward tube, and causal localization. We prove a rigidity result showing that any modification satisfying all three conditions must vanish identically. This establishes a structural obstruction linking analyticity and causal constraints in QFT. Building on this result, we provide a systematic classification of nontrivial hidden-variable extensions according to which analytic assumptions fail. We identify three distinct regimes: (i) delocalized modifications compatible with standard QFT, (ii) causally localized modifications that violate the spectral condition and introduce negative-frequency components, and (iii) localized modifications that necessarily break analyticity. These results show that nontrivial hidden-variable theories cannot be embedded within the standard analytic framework of relativistic QFT without violating at least one of its fundamental structural principles. The work provides a unified analytic perspective on the constraints governing hidden-variable extensions and clarifies the role of analyticity as a rigidity mechanism.
This work introduces a theoretical framework for nonlocal hidden-variable models based on “complex jammers”, defined over a structured parameter space extending standard space–time. The framework is designed to explore whether hidden nonlocal mechanisms can modify quantum correlations while remaining consistent with relativistic causality and the no-signalling principle. A central result establishes that exact operational indistinguishability from quantum mechanics forces the effective dynamics to reduce to the identity channel. This implies that any hidden mechanism that is completely invisible at the level of observable statistics must be dynamically trivial. Prior to this regime, we show that admissible dynamics is already strongly constrained: it must preserve all local marginals and can only act on correlations. Beyond equilibrium, the framework predicts a restricted class of deviations from quantum mechanics. In particular, we derive a minimal geometric mechanism leading to anisotropic corrections of the form cos²(θ), arising from axial symmetry defined by the experimental configuration. These deviations induce measurable, orientation-dependent distortions in Bell-type correlations. An explicit two-qubit model is constructed, and angle-dependent CHSH bounds are obtained. The results define a concrete experimental program based on high-precision Bell tests, capable of probing structured deviations from standard quantum predictions. The work does not propose a complete dynamical hidden-variable theory, but rather a set of physically motivated constraints on possible nonlocal extensions of quantum mechanics, together with falsifiable signatures that can be tested with current experimental platforms.
Relativistic causality in certain spacetime configurations permits jamming - superluminal causal influences that nevertheless do not enable superluminal signaling. We fully characterize the correlations compatible with relativistic causality (RC) by extending the operator framework of PRL 104, 140404. When the underlying state is required to be quantum, we prove that any nontrivial jamming - whether state-independent or state-dependent - necessarily leads to hidden superluminal signaling. Thus, the only consistent possibilities are standard quantum correlations without jamming or the full relativistically causal correlation set, with intermediate jamming extensions of quantum correlations leading to signaling. As an application of our characterization, we investigate the security of device-independent (DI) cryptographic primitives against adversaries constrained only by relativistic causality. We construct explicit RC attacks that break DI bit commitment and DI secret sharing in jamming geometries, even when these protocols remain secure against no-signaling adversaries. Our results show that security against relativistic adversaries requires behaviors to be specified together with the spacetime locations of their measurement events; input-output statistics alone are insufficient.