📝 SummarXiv

Abstract

In this article, we introduce No Global Counterfactual Consistency (NGCC), a new foundational no-go principle generalizing the recently proposed Circular Interaction-Free Paradox (CIFP). NGCC asserts that in any single-world interpretation of quantum mechanics that permits bounded-disturbance (epsilon-counterfactual) measurements, one cannot have a globally consistent assignment of outcomes for a closed network of counterfactual inferences. In essence, if multiple observers perform nearly interaction-free measurements around a closed loop (or any network containing cycles), their locally certain conclusions cannot all be mutually consistent in a single classical narrative. We formalize this as a circular consistency theorem and a family of exclusivity inequalities that any non-contextual, single-world hidden-variable model must satisfy. These constraints extend the CIFP beyond an n-lab ring to arbitrary network topologies, enforcing an NGCC bound on joint outcome probabilities. Quantum mechanics violates these bounds for sufficiently small epsilon, implying that no single-world, non-contextual model (even one allowing slight measurement disturbance) can reproduce the quantum predictions in such scenarios. Rigorous proofs are provided using graph-theoretic methods, semidefinite duality, and multi-cycle exclusivity structures.