Quantum Teleportation Advances: Energy Transfer and Wavefunction Collapse Reconfirmed — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 8, 2026• 0 citations

Abstract

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* $ \langle H_B \rangle_{\rho} - \langle H_B \rangle_{\rho'} < 0 $ where $\rho'$ 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 $ \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle) $. - Logical gate teleportation (Oxford): uses cluster-state graph codes; the mathematical core is the *stabilizer formalism* — Pauli group $ \{I, X, Y, Z\} $ with eigenvalues $ \pm 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

DOI: 10.5281/zenodo.23230027

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Published Oct 8, 2026• 0 citations

Publisher

Abstract

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 ( \langle H_B \rangle_{\rho} - \langle H_B \rangle_{\rho'} < 0 ) where (\rho') 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 ( \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle) ). - Logical gate teleportation (Oxford): uses cluster-state graph codes; the mathematical core is the stabilizer formalism — Pauli group ( {I, X, Y, Z} ) with eigenvalues ( \pm 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

DOI: 10.5281/zenodo.23230027

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|\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

\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

F = \langle \psi | \rho_{\text{out}} | \psi \rangle

, with

F=1

for ideal teleportation. Energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) to extract energy from a vacuum-like entangled state — quantified by energy gain

\Delta E = \langle H \rangle_{\text{out}} - \langle H \rangle_{\text{in}} > 0

under energy conditions. No new fundamental constants; relies on

SU(2)

rotation group and

2\times2

density matrices. CONNECTION: The teleportation unitary set

\{I, \sigma_x, \sigma_y, \sigma_z\}

corresponds to the Pauli matrices — generators of

SU(2)

, whose Lie Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

U \in \{I, X, Z, XZ\}

applied conditionally. Fidelity

F = |\langle \psi_{\text{in}} | \psi_{\text{out}} \rangle|^2

approaches 1 in ideal case; distance record 1,400 km via satellite (Micius) — no new fundamental constant, but scaling law for entanglement distribution:

P_{\text{success}} \propto e^{-\alpha L}

(attenuation), overcome by free-space channel. Energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) with negative energy density extracted from vacuum — quantified by conditional mutual information

I(A:C|B)

and energy bound

\langle E \rangle \geq - \frac{1}{\beta} I(A:C|B)

(thermodynamic cost). CONNECTION: No direct golden-ratio or base- Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)

|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)

. Teleportation fidelity

F = \langle\psi|\rho_{\text{out}}|\psi\rangle

— for ideal case

F=1

. Energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) with a quantum energy inequality:

\Delta E_A + \Delta E_B \geq 0

globally, but

\Delta E_B < 0

locally possible via negative energy density extracted from vacuum fluctuations — governed by the quantum energy condition (QEC) bound:

\Delta E \geq -\frac{c}{L}

(where

c

is a constant,

L

the system size). | CONNECTION: The Bell basis coefficients

1/\sqrt{2}

relate 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