Entangled Tunneling as a Coupled Gate: Differential Phase Signatures in Coincidence Rates of Spin-Correlated Particles (Paper IV/VII)

Closed-form derivation of the coincidence tunneling probability for spin-entangled particle pairs traversing spin-dependent barriers. The central result Pcoinc (φ, γ) decomposes into incoherent background plus coherent interference modulated by cos (φ + 2Δθ), where Δθ is the differential tunneling phase — a barrier property invisible to single-particle measurements but directly observable through entanglement. Numerical predictions for Co/Al₂O₃/Co magnetic tunnel junctions yield coincidence visibility >90% and modulation ratio R > 10⁴. Three experimental proposals: magnetic tunnel junctions with Cooper pair splitting, frustrated total internal reflection with photon pairs, and cold atoms in optical lattices. Paper IV of VII in the Δ-Gate theoretical core. Part of the Δ-Gate Formalism (DOI: 10. 5281/zenodo. 19103765). , , , , , , ,