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

Enso O. Torres Alegre

Paper

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

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.