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Canadian Journal of Physics

Quantum energy in quantum computers: insights from quantum energy teleportation

Kazuki Ikeda

Published Jul 16, 2025• 4 citations
Publisher

Abstract

Quantum energy teleportation (QET) is a quantum feedback protocol in which local measurements, classical communication, and preexisting entanglement enable the extraction of energy at a distant site, without transporting physical energy carriers. Originally conceived as a theoretical manifestation of Maxwell’s demon, QET has developed into a versatile tool for probing quantum correlations, diagnosing phase transitions, and powering emergent quantum thermodynamic technologies. This brief review provides a pedagogical introduction to the theoretical foundations and recent developments of QET, including quantum operations, entropic and fidelity-based bounds, and resource analyses involving quantum discord. Additionally, recent experimental realizations on superconducting quantum computers are revisited.

DOI
10.1139/cjp-2025-0120

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Quantum energy teleportation (QET) is a quantum feedback protocol in which local measurements, classical communication, and preexisting entanglement enable the extraction of energy at a distant site, without transporting physical energy carriers. Originally conceived as a theoretical manifestation of Maxwell’s demon, QET has developed into a versatile tool for probing quantum correlations, diagnosing phase transitions, and powering emergent quantum thermodynamic technologies. This brief review provides a pedagogical introduction to the theoretical foundations and recent developments of QET, including quantum operations, entropic and fidelity-based bounds, and resource analyses involving quantum discord. Additionally, recent experimental realizations on superconducting quantum computers are revisited.
In this work, we explore quantum energy teleportation (QET) protocols, focusing on their behavior at finite temperatures , in ground and excited states. We analyze the role of entanglement as a resource for QET, particularly in thermal states, and compare the performance of QET across these initial states. We then introduce a method to extract ground-state energy through a protocol that employs only quantum measurements, local operations, and classical communication (LOCC), without requiring the ground state to be quantum correlated either through entanglement or quantum discord. To illustrate this, we propose a minimal model comprising two interacting qubits. These findings indicate that, in addition to the established QET framework where quantum correlation serves as a resource, it is possible to extract energy from an product ground state. This broadens the scope of QET's applicability across diverse quantum systems.
Quantum energy teleportation (QET) is, from the operational viewpoint of distant protocol users, energy transportation via local operations and classical communication. QET has various links to fundamental research fields including black-hole physics, the quantum theory of Maxwell's demon, and quantum entanglement in condensed-matter physics. However, the energy that has been extracted using a previous QET protocol is limited by the distance between two protocol users; the upper bound of the energy being inversely proportional to the distance. In this paper, we prove that introducing squeezed vacuum states with local vacuum regions between the two protocol users overcomes this limitation, allowing energy teleportation over practical distances.
Quantum energy teleportation (QET) exploits the existence of correlations to enable remote energy transfer without the need for physical energy carriers between emitter and receiver. This paper presents a review of the thermodynamic foundations of QET and reviews its first experimental demonstration (performed using nuclear magnetic resonance), along with its implementation on publicly available superconducting quantum hardware. Additionally, we review an application of QET in the field of quantum thermodynamics as an efficient algorithmic cooling technique to cool down individual parts of interacting systems. Finally, we will review how QET can be employed to optimally generate exotic quantum states characterized by negative average stress–energy densities, offering a new operational approach to engineering such states that are promising in the context of semiclassical gravity.
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
Quantum energy teleportation (QET) is the phenomenon in which locally inaccessible energy is activated as extractable work through collaborative local operations and classical communication (LOCC) with an entangled partner. It closely resembles the more well-known quantum information teleportation (QIT) where quantum information can be sent through an entangled pair with LOCC. It is tempting to ask how QET is related to QIT. Here we report a first study of this connection. Despite the apparent similarity, we show that these two phenomena are not only distinct but moreover are mutually competitive. We show a perturbative trade-off relation between their performance in a thermal entangled chaotic many-body system, in which both QET and QIT are simultaneously implemented through a traversable wormhole in an emergent spacetime. Motivated by this example, we study a generic setup of two entangled qudits and prove a universal non-perturbative trade-off bound. It shows that for any teleportation protocol, the overall performance of QET and QIT together is constrained by the entanglement resource. We discuss some explanations of our results.
FINDING: Quantum teleportation transfers quantum *states* (information) via entanglement, not matter/energy; recent work extends this to teleporting *physical quantities* (energy) on superconducting hardware. | MATH: Core protocol uses Bell-state measurement (maximally entangled basis, dimension d=2 for qubits; generalized to d-dimensions), classical communication of 2 bits per teleported qubit, and unitary correction U ∈ {I, X, Z, XZ}. Fidelity F = |⟨ψ|ρ_out|ψ⟩|² ≥ 2/3 for classical bound; experimental fidelities often >0.9. Energy teleportation (arXiv:2301.02666) uses a quantum energy teleportation (QET) protocol: local measurement on one qubit of an entangled pair, then conditional unitary on the other, extracting positive energy ΔE > 0 from the vacuum/ground state. Key quantity: conditional mutual information or entanglement entropy S(ρ_A) − S(ρ_AB) governs extractable energy. | CONNECTION: Bell states are eigenvectors of Pauli matrices — roots of SU(2), isomorphic to quaternions ( Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com