FINDING: Quantum teleportation transfers quantum *state* (information), not matter — no particle traverses the channel; only a classical 2-bit message plus a pre-shared entangled pair is required. | MATH: Protocol (Bennett et al. 1993): Alice holds unknown state |ψ⟩ = α|0⟩ + β|1⟩ (|α|²+|β|²=1) and one qubit of a Bell pair |Φ⁺⟩ = (|00⟩+|11⟩)/√2. Joint Bell-basis measurement yields one of 4 outcomes {|Φ±⟩,|Ψ±⟩}, each probability 1/4. Alice sends 2 classical bits (log₂4 = 2). Bob applies one of {I, X, Z, XZ} to recover |ψ⟩ exactly. Fidelity F=1; no-cloning preserved (state destroyed at Alice). | CONNECTION: The 4 Bell states form an orthonormal basis of the 2-qubit Hilbert space ℂ²⊗ℂ² ≅ ℂ⁴ — a complete measurement basis. The 1/4 uniform outcome probability is the maximally-mixed (maximally-entangled) reference state ρ = I/4. This is the qubit analogue of a 4-fold symmetric point group (C₂ᵥ-like), and the Pauli group {I,X,Y,Z} is the order-4 operator set closing under multiplication. The √ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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