Operational Derivation of Born's Rule from Causal Consistency in Generalized Probabilistic Theories

• URL: http://arxiv.org/abs/2512.12636v2
• Date: Tue, 16 Dec 2025 08:58:35 GMT
• Title: Operational Derivation of Born's Rule from Causal Consistency in Generalized Probabilistic Theories
• Authors: Enso O. Torres Alegre,
• Abstract summary: We show that any admissible state-to-probability map must be affine under mixing.<n>We identify Born's rule as a causal fixed point among admissible probabilistic laws.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an operational derivation of Born's rule within finite-dimensional generalized probabilistic theories (GPTs), without assuming Hilbert-space structure. From a single causal requirement, namely causal consistency, together with sharp measurements, reversible symmetries, and no-signaling, we show that any admissible state-to-probability map must be affine under mixing; otherwise, its curvature enables superluminal signaling via steering. Using standard reconstruction results, affinity forces the probability assignment to coincide with the quadratic transition function of complex quantum theory. Our three-stage argument (operational assignment, causal-consistency constraints, and structural reconstruction) recovers complex quantum theory and identifies Born's rule as a causal fixed point among admissible probabilistic laws. We discuss limitations of the derivation and outline steering-based experiments that could bound deviations from affinity.

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