Quantum Teleportation Scales to City Distances and Transfers Energy — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Abstract

FINDING: Quantum teleportation has scaled from tabletop to metropolitan distances (270 m free-space, city-scale fiber entanglement) and extended from state transfer to energy/quantity transfer on superconducting hardware. | MATH: Bell-state measurement projects onto maximally entangled basis {|Φ±⟩=(|00⟩±|11⟩)/√2, |Ψ±⟩=(|01⟩±|10⟩)/√2}; protocol consumes 1 ebit + 2 classical bits to transmit 1 qubit (no-cloning bound: fidelity F ≤ 2/3 for classical channel, F→1 with entanglement). Energy teleportation injects E via local measurement, extracted remotely: ⟨E_out⟩ = -⟨H_B⟩ conditional on Alice's outcome. | CONNECTION: √2 normalization of Bell states = diagonal of unit square; the 2-bit/1-ebit/1-qubit accounting is a conservation law on Hilbert-space dimension (d² = d×d). No 0.618/1.618 signature in the protocol itself — the golden ratio is absent from teleportation algebra. | DEPTH: 6 --- **1. Key mathematical insight** Teleportation is not transport of matter or a signal — it is a *reso Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23830916

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Quantum Teleportation Scales to City Distances and Transfers Energy — E8 Intelligence Research

Andrew Stewart Caldin

Published Oct 31, 2026• 0 citations

Publisher

Abstract

FINDING: Quantum teleportation has scaled from tabletop to metropolitan distances (270 m free-space, city-scale fiber entanglement) and extended from state transfer to energy/quantity transfer on superconducting hardware. | MATH: Bell-state measurement projects onto maximally entangled basis {|Φ±⟩=(|00⟩±|11⟩)/√2, |Ψ±⟩=(|01⟩±|10⟩)/√2}; protocol consumes 1 ebit + 2 classical bits to transmit 1 qubit (no-cloning bound: fidelity F ≤ 2/3 for classical channel, F→1 with entanglement). Energy teleportation injects E via local measurement, extracted remotely: ⟨E_out⟩ = -⟨H_B⟩ conditional on Alice's outcome. | CONNECTION: √2 normalization of Bell states = diagonal of unit square; the 2-bit/1-ebit/1-qubit accounting is a conservation law on Hilbert-space dimension (d² = d×d). No 0.618/1.618 signature in the protocol itself — the golden ratio is absent from teleportation algebra. | DEPTH: 6 --- 1. Key mathematical insight Teleportation is not transport of matter or a signal — it is a *reso Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

DOI: 10.5281/zenodo.23830916

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FINDING: Quantum teleportation transmits quantum states (not matter) over distance via entanglement; recent work extends this to teleporting energy on superconducting hardware. | MATH: Core protocol uses Bell state measurement (BSM) — a projection onto maximally entangled basis: $|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)$ , $|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)$ . 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.comFINDING: Quantum teleportation transmits quantum states (not matter) over distance via entanglement; recent work extends this to teleporting energy on superconducting hardware. | MATH: Core protocol uses Bell state measurement (BSM) — a projection onto maximally entangled basis: $|\Phi^\pm\rangle = \frac{1}{\sqrt{2}}(|00\rangle \pm |11\rangle)$, $|\Psi^\pm\rangle = \frac{1}{\sqrt{2}}(|01\rangle \pm |10\rangle)$. 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

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Andrew Stewart Caldin

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|\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

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

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

(Bell-state measurement, two classical bits per qubit); energy teleportation uses local operations and classical communication (LOCC) with conditional energy extraction

\Delta E = -\frac{1}{\beta}\ln(\text{Tr}[\rho e^{-\beta H}])

(from arXiv:2301.02666v5); entanglement entropy

S = -\text{Tr}[\rho \ln \rho]

; no equation for distance scaling beyond channel loss

\eta \propto e^{-\alpha L}

. | 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

\mathbb{Z}_2 \times \mathbb{Z}_2

, a crystallographic point group 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

(max classical bound

F \leq 2/3

); Bell-state measurement projects onto maximally entangled basis

\{\Phi^\pm, \Psi^\pm\}

; energy teleportation (arXiv:2301.02666) uses local operations and classical communication (LOCC) with energy extracted via conditional unitary

U(\theta)

where

\theta

encodes measurement outcome — no net energy transported, only correlations. | CONNECTION: Bell states live in

\mathbb{C}^2 \otimes \mathbb{C}^2

— the root system

A_1 \times A_1

(tetragonal symmetry, 4-fold). The 1,400 km path and 2/3 classical bound echo the golden ratio's reciprocal

1/\varphi \approx 0.618

in the sense that

2/3 \approx 0.667

is the classical limit — not a direc Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com