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Quantum Teleportation Advances: From Qubits to Logical Gates and Energy — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 19, 2026• 0 citations
Publisher

Abstract

FINDING: Quantum teleportation has advanced from information transfer to energy teleportation on superconducting hardware, while Oxford demonstrated teleportation of logical gates — not just qubits. | MATH: The core invariant is the Bell-state measurement projection: \(|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)\), with teleportation fidelity \(F = \frac{1}{2} + \frac{2}{3}|\langle\psi_{in}|\psi_{out}\rangle|^2\) for qubits. Energy teleportation (arXiv:2301.02666) exploits negative energy density via local operations and classical communication (LOCC), quantified by the conditional entropy \(S(A|B) = S(\rho_{AB}) - S(\rho_B) < 0\) — the resource is not entanglement alone but *quantum discord* in the energy eigenbasis. The W-state (mentioned in German source) scales as \(|W_N\rangle = \frac{1}{\sqrt{N}}\sum_{i=1}^N |0...1_i...0\rangle\), with entanglement entropy \(S = \log_2 N\) for N parties — robust against particle loss, unlike GHZ states. | CONNECTION: The W-state' Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI
10.5281/zenodo.23465114

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FINDING: Quantum teleportation transmits state (not matter) over 1,400 km; energy teleportation demonstrated on superconducting hardware; no classical information moves faster than light. | MATH: Teleportation fidelity F=⟨ψ∣ρout∣ψ⟩F = \langle\psi|\rho_{\text{out}}|\psi\rangleF=⟨ψ∣ρout​∣ψ⟩ (Bell-state measurement, two classical bits per qubit); energy teleportation uses local operations and classical communication (LOCC) with conditional energy extraction ΔE=−1βln⁡(Tr[ρe−βH])\Delta E = -\frac{1}{\beta}\ln(\text{Tr}[\rho e^{-\beta H}])ΔE=−β1​ln(Tr[ρe−βH]) (from arXiv:2301.02666v5); entanglement entropy S=−Tr[ρln⁡ρ]S = -\text{Tr}[\rho \ln \rho]S=−Tr[ρlnρ]; no equation for distance scaling beyond channel loss η∝e−αL\eta \propto e^{-\alpha L}η∝e−αL. | CONNECTION: None intrinsic — teleportation is a discrete operation (Bell basis, 4 outcomes) with no continuous ratio; however, the two classical bits per qubit ratio (2:1) echoes binary/ternary symmetry, and the Bell basis is a 4-element group isomorphic to Z2×Z2\mathbb{Z}_2 \times \mathbb{Z}_2Z2​×Z2​, a crystallographic point group 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; energy teleportation demonstrated on superconducting hardware; no violation of no-communication theorem. | MATH: Teleportation fidelity F=⟨ψ∣ρout∣ψ⟩F = \langle\psi|\rho_{\text{out}}|\psi\rangleF=⟨ψ∣ρout​∣ψ⟩ (Bell-state measurement success probability 1/41/41/4 per attempt for qubits); entanglement resource: Bell pair ∣Φ+⟩=12(∣00⟩+∣11⟩)|\Phi^+\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle)∣Φ+⟩=2​1​(∣00⟩+∣11⟩); classical communication cost: 2 bits per teleported qubit; energy teleportation (arXiv:2301.02666v5) uses local operations + classical communication (LOCC) to extract energy from vacuum fluctuations via negative energy density regions — quantified by energy density ⟨T00⟩<0\langle T_{00}\rangle < 0⟨T00​⟩<0 in a narrow window, with extracted energy Eext=ℏcd2⋅O(1)E_{\text{ext}} = \frac{\hbar c}{d^2} \cdot \mathcal{O}(1)Eext​=d2ℏc​⋅O(1) where ddd is the separation scale. | CONNECTION: The Bell basis itself is a discrete symmetry group of order 4 (isomorphic to Z2×Z2\mathbb{Z}_2 \times \mathbb{Z}_2Z2​×Z2​) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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