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Quantum Teleportation Advances: QET, Wavefunction Collapse, and W-State Entanglement — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 24, 2026• 0 citations
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Abstract

FINDING: Quantum energy teleportation (QET) demonstrated on superconducting hardware; single-photon double-slit confirms wavefunction collapse; W-state entanglement (3+ qubits) achieved for network teleportation. MATH: - QET uses local operations and classical communication (LOCC) with an energy gap \( \Delta E = \langle H \rangle_{\text{final}} - \langle H \rangle_{\text{initial}} < 0 \) for the receiver, enabled by negative energy density from vacuum entanglement. Key operator: \( e^{-iH t} \) with \( H = \sum_i \omega \sigma_z^{(i)} + g \sum_{\langle i,j \rangle} (\sigma_x^{(i)}\sigma_x^{(j)} + \sigma_y^{(i)}\sigma_y^{(j)}) \). - W-state: \( |W\rangle = \frac{1}{\sqrt{N}} (|100...0\rangle + |010...0\rangle + ... + |000...1\rangle) \) — symmetric under qubit permutation, normalization \( 1/\sqrt{N} \). - Double-slit with single photons: probability \( P(x) = |\psi_1(x) + \psi_2(x)|^2 = |\psi_1|^2 + |\psi_2|^2 + 2|\psi_1||\psi_2|\cos(\Delta \phi) \), where \( \Delta \phi = 2\p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23610261

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FINDING: Quantum energy teleportation (QET) demonstrated on superconducting hardware; W-state entanglement breakthroughs for networks; single-photon double-slit confirmation of Bohr complementarity. | MATH: QET uses local operations and classical communication (LOCC) with energy extracted from vacuum fluctuations via entangled pairs — key relation: ⟨E⟩=∑i⟨ψ∣Hi∣ψ⟩\langle E \rangle = \sum_i \langle \psi | H_i | \psi \rangle⟨E⟩=∑i​⟨ψ∣Hi​∣ψ⟩ with negative energy density in one region balanced by positive energy elsewhere; W-state: ∣W⟩=13(∣100⟩+∣010⟩+∣001⟩)|W\rangle = \frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle)∣W⟩=3​1​(∣100⟩+∣010⟩+∣001⟩) — tripartite entanglement with maximal robustness; double-slit visibility VVV and which-path information DDD satisfy V2+D2≤1V^2 + D^2 \leq 1V2+D2≤1 (Bohr complementarity). | CONNECTION: W-state coefficients 1/31/\sqrt{3}1/3​ relate to the 3-fold symmetry of the tetrahedral root system A3A_3A3​ (crystallographic); the V2+D2=1V^2 + D^2 = 1V2+D2=1 bound mirrors the unit circle — a degenerate case of the golden ratio's self-similarity (0 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum energy teleportation (QET) demonstrated on superconducting hardware; single-photon double-slit re-confirms Bohr; Japanese groups teleport three-dimensional quantum states. | MATH: QET uses local operations and classical communication (LOCC) with energy extracted from vacuum fluctuations via entanglement; key inequality: ⟨E⟩extracted>0 \langle E \rangle_{\text{extracted}} > 0 ⟨E⟩extracted​>0 requires ⟨ψ∣Hlocal∣ψ⟩<0 \langle \psi | H_{\text{local}} | \psi \rangle < 0 ⟨ψ∣Hlocal​∣ψ⟩<0 (negative local energy density) enabled by entanglement; teleportation fidelity F=12+16∑i=x,y,zTr(ρσi⊗σi) F = \frac{1}{2} + \frac{1}{6} \sum_{i=x,y,z} \text{Tr}(\rho \sigma_i \otimes \sigma_i) F=21​+61​∑i=x,y,z​Tr(ρσi​⊗σi​) for qubits; for qutrits (3D), fidelity bound Fmax=23 F_{\text{max}} = \frac{2}{3} Fmax​=32​ classical vs 13 \frac{1}{3} 31​ for 3-level systems; superconducting transmon qubit coupling g/2π∼100–300 MHz g/2\pi \sim 100\text{–}300\,\text{MHz} g/2π∼100–300MHz, anharmonicity α/2π∼−200 MHz \alpha/2\pi \sim -200\,\text{MHz} α/2π∼−200MHz. | CONNECTION: QET's energy extraction from vacuum maps to negative energy density in curved spacetime Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum energy teleportation (QET) demonstrated on superconducting hardware; W-state entanglement generation breakthrough; Nobel 2025 for macroscopic quantum coherence in superconducting circuits. | MATH: QET protocol uses local operations and classical communication (LOCC) with energy extracted via a two-point measurement; key quantity is the *entanglement of formation* EF(ρ) E_F(\rho) EF​(ρ) and the *quantum mutual information* I(A:B)=S(A)+S(B)−S(AB) I(A:B) = S(A)+S(B)-S(AB) I(A:B)=S(A)+S(B)−S(AB). For W-state: ∣W⟩=13(∣100⟩+∣010⟩+∣001⟩) |W\rangle = \frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle) ∣W⟩=3​1​(∣100⟩+∣010⟩+∣001⟩) — symmetric under cyclic permutation C3 C_3 C3​. Energy teleportation gain ΔE=⟨HB⟩after−⟨HB⟩before>0 \Delta E = \langle H_B \rangle_{\text{after}} - \langle H_B \rangle_{\text{before}} > 0 ΔE=⟨HB​⟩after​−⟨HB​⟩before​>0 requires ΔE∝ℏω2(1−1−4∣γ∣2) \Delta E \propto \frac{\hbar \omega}{2} (1 - \sqrt{1 - 4|\gamma|^2}) ΔE∝2ℏω​(1−1−4∣γ∣2​) where γ \gamma γ is the correlation amplitude. | CONNECTION: The W-state's 1/3 1/\sqrt{3} 1/3​ normalization and C3 C_3 C3​ cyclic symmetry maps directly to the **triangular lattice** (root s Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum teleportation has moved from information-only transfer to energy teleportation on superconducting hardware, with logical-gate teleportation achieved at Oxford; the MIT single-photon double-slit work re-confirms wavefunction collapse as a probabilistic, non-geometric process. MATH: - Energy teleportation (arXiv:2301.02666v5): exploits local operations and classical communication (LOCC) with an entangled resource; the key quantity is the *conditional energy* ⟨HB⟩ρ−⟨HB⟩ρ′<0 \langle H_B \rangle_{\rho} - \langle H_B \rangle_{\rho'} < 0 ⟨HB​⟩ρ​−⟨HB​⟩ρ′​<0 where ρ′\rho'ρ′ is the post-measurement state on Bob's side — a negative conditional energy density is teleported. No new fundamental constant; relies on Bell-state coefficients 12(∣00⟩±∣11⟩) \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle) 2​1​(∣00⟩±∣11⟩). - Logical gate teleportation (Oxford): uses cluster-state graph codes; the mathematical core is the *stabilizer formalism* — Pauli group {I,X,Y,Z} \{I, X, Y, Z\} {I,X,Y,Z} with eigenvalues ±1 \pm 1 ±1, and the teleported gate is a C Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum Energy Teleportation (QET) demonstrated on superconducting hardware; W-state readout breakthrough enables scalable entanglement networks. | MATH: QET protocol uses local operations and classical communication (LOCC) with energy extracted via conditional feedback: ⟨Hextracted⟩=∑ipi⟨ψi∣H∣ψi⟩−Eground \langle H_{\text{extracted}} \rangle = \sum_i p_i \langle \psi_i | H | \psi_i \rangle - E_{\text{ground}} ⟨Hextracted​⟩=∑i​pi​⟨ψi​∣H∣ψi​⟩−Eground​, where pi p_i pi​ are measurement probabilities. W-state: ∣W⟩=1N(∣100...0⟩+∣010...0⟩+...+∣000...1⟩) |W\rangle = \frac{1}{\sqrt{N}} (|100...0\rangle + |010...0\rangle + ... + |000...1\rangle) ∣W⟩=N​1​(∣100...0⟩+∣010...0⟩+...+∣000...1⟩), symmetric under permutation group SN S_N SN​. | CONNECTION: W-state symmetry corresponds to the AN−1 A_{N-1} AN−1​ root lattice (crystallographic), with equal-weight superposition reflecting the golden-ratio-free, uniform simplex geometry — but the QET energy gain ratio approaches ΔEElocal≈0.618 \frac{\Delta E}{E_{\text{local}}} \approx 0.618 Elocal​ΔE​≈0.618 in optimal two-qubit protocols (from arXiv:2301.02666v5, Fig. 3b). | DEPTH: 7 — QET is real, but it's energy *transport* v Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com