Quantum Teleportation: Entanglement, Energy Transfer, and 1,400 km State Transmission — E8 Intelligence Research

FINDING: Quantum teleportation transfers quantum states (not matter) via entanglement, with recent demonstrations of energy teleportation on superconducting hardware and long-distance (1,400 km) state transfer. | MATH: Core formalism: Bell-state measurement projects onto maximally entangled basis {|Φ⁺⟩, |Φ⁻⟩, |Ψ⁺⟩, |Ψ⁻⟩}; teleportation fidelity F = ⟨ψ|ρ_out|ψ⟩; for ideal case F=1, for classical limit F≤2/3. Energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) with Hamiltonian H = H_A + H_B + V_AB, extracting energy ΔE = ⟨ψ_final|H|ψ_final⟩ − ⟨ψ_initial|H|ψ_initial⟩ < 0 from vacuum-like state via entanglement. | CONNECTION: The four Bell states correspond to the Klein four-group Z₂×Z₂ — a finite abelian group with order 4, isomorphic to the symmetry group of a rectangle (D₂). This is a crystallographic point group (2/m in Hermann–Mauguin notation). The 2×2 structure of Bell basis mirrors the root system A₁×A₁ (two orthogonal rank-1 roots), and Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com