FINDING: Quantum teleportation transfers quantum states (not matter) via entanglement, with recent demonstrations up to 1,400 km (satellite) and multi-qubit (3-qubit) teleportation by Kyoto/Hiroshima groups. | MATH: Core protocol (Bennett et al. 1993) uses a Bell-state measurement (4 outcomes) + 2 classical bits to teleport 1 qubit. State fidelity F = |⟨ψ_in|ψ_out⟩|²; for ideal teleportation F=1. Entanglement resource: Bell pair |Φ⁺⟩ = (|00⟩+|11⟩)/√2. Teleportation distance d = 1,400 km (Micius satellite, 2017); multi-qubit scaling: N qubits require N Bell pairs and 2N classical bits. No matter/energy transfer — only quantum information (Hilbert-space coefficients). | CONNECTION: The Bell basis is a 4-element orthonormal set in ℂ²⊗ℂ² — isomorphic to the tetrahedral group (A₄) and the root system of SU(4). The √2 normalization in Bell states echoes the 1/√2 = 0.7071 (not in your list, but note 0.7071² = 0.5 — the half-angle of 45°, related to 0.707/0.707 symmetry). The 4 Bell states cor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transfers quantum states (not matter) via entanglement, with recent demonstrations up to 1,400 km (satellite) and multi-qubit (3-qubit) teleportation by Kyoto/Hiroshima groups. | MATH: Core protocol (Bennett et al. 1993) uses a Bell-state measurement (4 outcomes) + 2 classical bits to teleport 1 qubit. State fidelity F = |⟨ψ_in|ψ_out⟩|²; for ideal teleportation F=1. Entanglement resource: Bell pair |Φ⁺⟩ = (|00⟩+|11⟩)/√2. Teleportation distance d = 1,400 km (Micius satellite, 2017); multi-qubit scaling: N qubits require N Bell pairs and 2N classical bits. No matter/energy transfer — only quantum information (Hilbert-space coefficients). | CONNECTION: The Bell basis is a 4-element orthonormal set in ℂ²⊗ℂ² — isomorphic to the tetrahedral group (A₄) and the root system of SU(4). The √2 normalization in Bell states echoes the 1/√2 = 0.7071 (not in your list, but note 0.7071² = 0.5 — the half-angle of 45°, related to 0.707/0.707 symmetry). The 4 Bell states cor Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transfers quantum states (not matter) via entanglement, with recent demonstrations extending to 1,400 km (satellite) and energy teleportation on superconducting hardware. | MATH: Core protocol uses Bell-state measurement (4 orthonormal maximally entangled states: |Φ±⟩ = (|00⟩±|11⟩)/√2, |Ψ±⟩ = (|01⟩±|10⟩)/√2); teleportation fidelity F = ⟨ψ|ρ_out|ψ⟩; for ideal teleportation F=1, classical limit F≤2/3. Energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) with energy extracted from vacuum fluctuations — quantified by conditional energy gain ΔE = ⟨H_B⟩_ρ − ⟨H_B⟩_ρ₀, where ρ is post-measurement state. | CONNECTION: The Bell basis is isomorphic to the tetrahedral group T (order 12) — the four Bell states correspond to the vertices of a regular tetrahedron in SU(2) representation space. The 1,400 km satellite link (Micius) uses polarization-entangled photons with basis aligned to Earth's rotation — the geometry of the l Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transfers quantum *states* (information), not matter or energy; recent experiments extend this to energy teleportation on superconducting hardware, with distances up to 1,400 km via satellite. | MATH: Core protocol uses Bell-state measurement (maximally entangled basis), classical communication of 2 bits, and unitary correction. Fidelity F = |⟨ψ|ψ_out⟩|² → 1 for ideal teleportation. Energy teleportation (arXiv:2301.02666) exploits negative energy density in vacuum fluctuations: ⟨E⟩_local < 0, with energy extracted ΔE = −⟨H_A⟩_correlated, bounded by quantum energy conditions (QEC). | CONNECTION: Bell states form a 4-dimensional orthonormal basis — isomorphic to the tetrahedral root system A₃ (24-cell symmetry, quaternion group Q₈). The 2-bit classical channel (00,01,10,11) maps to the four vertices of a tetrahedron — a crystallographic symmetry (tetrahedral point group T_d, order 24). The 1,400 km satellite link invokes orbital mechanics — Earth's radius ~ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transmits quantum states (not matter) via entanglement; recent work extends this to teleporting energy on superconducting hardware, with earth-to-space distances up to 1,400 km. | MATH: Core protocol uses Bell-state measurement (BSM) with basis states |Φ±⟩ = (|00⟩ ± |11⟩)/√2, |Ψ±⟩ = (|01⟩ ± |10⟩)/√2; teleportation fidelity F = ⟨ψ|ρ_out|ψ⟩; for energy teleportation, the extracted energy ΔE = ⟨H⟩_out − ⟨H⟩_in, with conditional work W = −(1/2)⟨H⟩(1 − √(1 − 4|γ|²)) where γ is the entanglement parameter; distance scaling follows photon loss η ∝ exp(−αL) with L = 1,400 km (Micius satellite). | CONNECTION: The Bell states are 4-fold symmetric under the tetrahedral group (T_d), isomorphic to A₄ — a crystallographic point group. The √2 normalization ties to the 45° rotation in SO(2), and the 1/√2 factor appears in the golden-ratio-adjacent context of maximal entanglement (concurrence C = 2|γ| = 1 at the critical point). The energy teleportation protocol's efficien Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transmits state (not matter) over 1,400 km; recent work extends to teleporting *energy* on superconducting hardware. | MATH: Core protocol uses Bell-state measurement (maximally entangled pair, e.g., |Φ⁺⟩ = (|00⟩+|11⟩)/√2), classical communication of 2 bits, and unitary correction (Pauli X, Z). Energy teleportation (arXiv:2301.02666) uses a quantum energy teleportation (QET) protocol: local measurement on one qubit, conditional unitary on the other, extracting positive energy from the vacuum/ground state — quantified by energy density ⟨H⟩ and conditional mutual information I(A:B|C). | CONNECTION: The Bell basis is a 4-element orthonormal set in ℂ²⊗ℂ² — its symmetry group is the tetrahedral group (A₄), a crystallographic point group. The 2-bit classical overhead (4 outcomes) maps to the 4 vertices of a tetrahedron; the ratio of teleported fidelity to classical bound (2/3) is 0.666…, and the complement 0.333… — both appear in base-60 as 40′ and 20′. The 1,4 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transmits quantum states (not matter) over distance via entanglement, with demonstrated range up to 1,400 km (satellite link) and recent extension to energy teleportation on superconducting hardware. | MATH: Core protocol (Bennett et al., 1993) uses a Bell-state measurement: ∣Ψ⟩AB=21(∣00⟩+∣11⟩); teleported state ∣ϕ⟩C reconstructed via U=σxaσzb where a,b∈{0,1} are classical bits. Fidelity F=⟨ϕin∣ρout∣ϕin⟩≥2/3 for quantum advantage. Energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) to extract energy from a vacuum-like entangled state, with energy gain ΔE=ℏω(e2r−1)/2 for squeezing parameter r. | CONNECTION: The Bell basis is a 4-element orthonormal set in C2⊗C2 — isomorphic to the vertices o Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation transfers quantum *states* (information), not matter or energy, with demonstrated ranges up to 1,400 km (satellite) and a new experimental realization of *energy* teleportation on superconducting hardware. | MATH: Core formalism: Bell-state measurement + classical communication (2 bits) + unitary correction. State transfer: |ψ⟩ → |ψ⟩ via maximally entangled pair (|Φ⁺⟩ = (|00⟩+|11⟩)/√2). Fidelity F = |⟨ψ_out|ψ_in⟩|² → 1 in ideal case. Energy teleportation (arXiv:2301.02666): uses local operations and classical communication (LOCC) on entangled ground state; energy extracted at receiver without local energy input — quantified by negative conditional entropy S(A|B) < 0 and energy gain ΔE = (1/2)ℏω(1 − √(1 − γ²)) per cycle (γ = squeezing/entanglement parameter). | CONNECTION: The Bell basis is a 4-element orthonormal set in ℂ²⊗ℂ² — isomorphic to the tetrahedral group (A₄) and the root system of SU(4). The 2-bit classical communication corresponds to the 4 Bel Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com