Bipartite Correlations through Enriched System Information in Phase-Coherent Amplitudes

This work presents a geometrically explicit representation of spin and polarization measurements in which the state of an individual particle is described by a continuous directional amplitude defined on the unit sphere. Measurement outcomes are modeled as local projection operations acting on these amplitudes, with statistical predictions obtained through averaging over preparation-dependent distributions. Within this formulation, the correlation structure of entangled photon pairs is derived directly from phase-coherent amplitude overlaps, where phase information is encoded geometrically through relative orientation. The resulting expression reproduces the standard quantum correlation function and exactly saturates the Tsirelson bound, without requiring additional assumptions beyond local projection geometry and phase tracking. The analysis provides a unified geometric description of Stern–Gerlach filtering, polarization, and bipartite correlations, highlighting how phase coherence at the amplitude level governs the formation of quantum statistics prior to probability assignment.