Quantum Teleportation: Entanglement, Classical Bits, and Tetrahedral Symmetry — E8 Intelligence Research

FINDING: Quantum teleportation is a protocol for transferring an unknown quantum state using shared entanglement and classical communication — not instantaneous transport of matter. | MATH: Bell state basis: |Φ⁺⟩ = (|00⟩ + |11⟩)/√2; teleportation requires 2 classical bits + 1 ebit (maximally entangled pair); measurement in Bell basis projects onto 4 orthogonal states; Pauli corrections: X, Z, XZ, I. | CONNECTION: The 4 Bell states form a tetrahedral symmetry group (S₄) — isomorphic to the rotational symmetry of a cube/octahedron (crystallographic point group O_h). The √2 normalization is the same ratio appearing in the diagonal of a unit square — a 45° rotation symmetry. | DEPTH: 7 --- **Detailed mathematical extraction:** 1. **Core protocol (Bennett et al. 1993):** - Alice holds qubit |ψ⟩ = α|0⟩ + β|1⟩ (|α|² + |β|² = 1). - Shared entangled pair: |Φ⁺⟩_AB = (|0⟩_A|0⟩_B + |1⟩_A|1⟩_B)/√2. - Total state: |ψ⟩_C ⊗ |Φ⁺⟩_AB. - Alice performs Bell measurement on qubits C Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com