Quantum Teleportation of Energy Achieved via Superconducting W-State Entanglement — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 8, 2026• 0 citations

Abstract

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* $ E_F(\rho) $ and the *quantum mutual information* $ I(A:B) = S(A)+S(B)-S(AB) $. For W-state: $ |W\rangle = \frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle) $ — symmetric under cyclic permutation $ C_3 $. Energy teleportation gain $ \Delta E = \langle H_B \rangle_{\text{after}} - \langle H_B \rangle_{\text{before}} > 0 $ requires $ \Delta E \propto \frac{\hbar \omega}{2} (1 - \sqrt{1 - 4|\gamma|^2}) $ where $ \gamma $ is the correlation amplitude. | CONNECTION: The W-state's $ 1/\sqrt{3} $ normalization and $ C_3 $ 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

DOI: 10.5281/zenodo.23229497

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Quantum Teleportation of Energy Achieved via Superconducting W-State Entanglement — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 8, 2026• 0 citations

Publisher

Abstract

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 ( E_F(\rho) ) and the quantum mutual information ( I(A:B) = S(A)+S(B)-S(AB) ). For W-state: ( |W\rangle = \frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle) ) — symmetric under cyclic permutation ( C_3 ). Energy teleportation gain ( \Delta E = \langle H_B \rangle_{\text{after}} - \langle H_B \rangle_{\text{before}} > 0 ) requires ( \Delta E \propto \frac{\hbar \omega}{2} (1 - \sqrt{1 - 4|\gamma|^2}) ) where ( \gamma ) is the correlation amplitude. | CONNECTION: The W-state's ( 1/\sqrt{3} ) normalization and ( C_3 ) 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

DOI: 10.5281/zenodo.23229497

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\langle H_{\text{extracted}} \rangle = \sum_i p_i \langle \psi_i | H | \psi_i \rangle - E_{\text{ground}}

, where

p_i

are measurement probabilities. W-state:

|W\rangle = \frac{1}{\sqrt{N}} (|100...0\rangle + |010...0\rangle + ... + |000...1\rangle)

, symmetric under permutation group

S_N

. | CONNECTION: W-state symmetry corresponds to the

A_{N-1}

root lattice (crystallographic), with equal-weight superposition reflecting the golden-ratio-free, uniform simplex geometry — but the QET energy gain ratio approaches

\frac{\Delta E}{E_{\text{local}}} \approx 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

\rho \to \sum_i K_i \rho K_i^\dagger

with Kraus operators

K_i = \langle i| U |\psi\rangle

; energy teleportation gain

\Delta E = \text{Tr}[\rho H] - \text{Tr}[\rho' H] > 0

requires negative conditional energy

\langle H_B \rangle_{\text{cond}} < 0

. Double-slit: visibility

V = (I_{\max} - I_{\min})/(I_{\max} + I_{\min})

, complementarity

V^2 + D^2 \leq 1

(D = distinguishability). W-state:

|W\rangle = (|100\rangle + |010\rangle + |001\rangle)/\sqrt{3}

— symmetric under particle permutations, maximal multipartite entanglement. | CONNECTION: W-state normalization

1/\sqrt{3}

links to triangular lattice coordination num Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

\langle E \rangle = \sum_i \langle \psi | H_i | \psi \rangle

with negative energy density in one region balanced by positive energy elsewhere; W-state:

|W\rangle = \frac{1}{\sqrt{3}}(|100\rangle + |010\rangle + |001\rangle)

— tripartite entanglement with maximal robustness; double-slit visibility

V

and which-path information

D

satisfy

V^2 + D^2 \leq 1

(Bohr complementarity). | CONNECTION: W-state coefficients

1/\sqrt{3}

relate to the 3-fold symmetry of the tetrahedral root system

A_3

(crystallographic); the

V^2 + D^2 = 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

T_{00}(x)

and its commutator with the Hamiltonian. Key inequality:

\langle E \rangle_{\text{final}} < \langle E \rangle_{\text{initial}}

for the receiver, enabled by negative energy density from the vacuum fluctuation suppression. The teleported energy

\Delta E

scales with the entanglement negativity

\mathcal{N}

and the coupling strength

g

of the measurement:

\Delta E \propto g^2 \mathcal{N}

. No explicit constants like 0.618 or 1.618 appear. | CONNECTION: No direct geometric harmony ratios found. However, the protocol's reliance on vacuum structure and local operations suggests a lattice symmetry: the qubits are arranged in a 1D chain with nearest-neighbor cou Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

\langle E \rangle = \langle \psi | H_B | \psi \rangle

where

H_B

is the receiver's Hamiltonian, achieved via a two-qubit protocol with ground state entanglement. The protocol uses a unitary operation

U_A(\theta)

on sender's qubit (parameter

\theta

controlling energy extraction) and a conditional unitary

U_B

on receiver's qubit, with classical communication of measurement outcome. The energy gain is quantified by

\Delta E = \langle \psi' | H_B | \psi' \rangle - \langle \psi_0 | H_B | \psi_0 \rangle > 0

for optimal

\theta

. | CONNECTION: The protocol relies on maximally entangled Bell states, which are symmetric under the tetrahedral group (crystallographic point group Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com