Quantum Energy Teleportation (QET)

• Quantum Energy Teleportation (QET) is a protocol that exploits quantum entanglement and local operations with classical communication to remotely extract energy without moving physical carriers.
• QET leverages local measurements and conditional unitary feedback to produce discrete negative-energy pockets, achieving extraction efficiencies up to around 35% in experimental settings.
• Experimental implementations in superconducting circuits and NMR systems validate QET's potential in enhancing quantum thermodynamics, cooling, and secure quantum network protocols.

Quantum Energy Teleportation (QET) is a quantum protocol enabling the remote activation and extraction of energy from one subsystem by another, using only local operations and classical communication (LOCC) in the presence of quantum correlations or entanglement. QET does not require any physical energy or particle carriers traversing the distance between sender and receiver; instead, it exploits nonlocal quantum correlations present in the ground or thermal state of a many-body system. QET provides a mechanism for enabling on-demand local energy extraction (as work) that would otherwise be forbidden by the strong local passivity of closed-system ground states. This protocol is of central importance in quantum thermodynamics, quantum information theory, and foundational studies of quantum energy flows.

1. Foundational Principles and Formalism

The canonical QET protocol involves two parties, Alice (A) and Bob (B), operating on spatially separated subsystems of an interacting Hamiltonian $H=H_A+H_B+V_{AB}$, where $[H_A+H_B,V_{AB}]\neq0$ ensures ground-state entanglement. The sequence of operations is:

1. Alice performs a local quantum measurement $M_A(\mu)$ on her subsystem. This action injects energy $E_{\text{in}}$ into $A$ and disturbs quantum correlations with $B$.
2. Alice communicates her measurement outcome $\mu$ to Bob via a classical channel; no quantum information or energy passes through the channel.
3. Bob performs a conditional local unitary $U_B(\mu)$ on his subsystem, designed to exploit the post-measurement correlations and reduce his local energy, effectively extracting $E_{\text{out}}>0$ as work.

The average teleported energy is given by: $$E_{\rm QET} = \sum_\mu p_\mu \left[ \operatorname{Tr}(H_B\,\rho_{B|\mu}) - \operatorname{Tr}(H_B\,U_B(\mu)\,\rho_{B|\mu}\,U_B^\dagger(\mu)) \right]$$ where $[H_A+H_B,V_{AB}]\neq0$0 is the postmeasurement state of $[H_A+H_B,V_{AB}]\neq0$1 after Alice’s outcome $[H_A+H_B,V_{AB}]\neq0$2 (Wang et al., 2024, Ikeda et al., 2023, Ragula et al., 7 May 2025).

Bob's action always results in a discrete negative-energy pocket in his local region, offset (globally) by the positive energy injected at Alice. No physical excitation traverses the system; causality and energy conservation are rigorously maintained (Ikeda et al., 2023, Ragula et al., 7 May 2025).

2. Resource Theory: Entanglement, Mutual Information, and Discord

The essential resource for QET is the presence of nonclassical correlations, typically quantified by entanglement entropy, mutual information, or quantum discord between $[H_A+H_B,V_{AB}]\neq0$3 and $[H_A+H_B,V_{AB}]\neq0$4. In gapped spin chains and minimal qubit models, ground-state entanglement is a necessary prerequisite: extracted energy $[H_A+H_B,V_{AB}]\neq0$5 scales quadratically with entanglement entropy $[H_A+H_B,V_{AB}]\neq0$6, bounded by (Hotta, 2013): $[H_A+H_B,V_{AB}]\neq0$7 where $[H_A+H_B,V_{AB}]\neq0$8 is the operator norm of Bob's local energy operator.

At finite temperature, when entanglement vanishes above a threshold $[H_A+H_B,V_{AB}]\neq0$9, quantum discord or nonzero mutual information may still enable QET—though in certain cases discord alone is insufficient, and protocols must be optimized to exploit thermal resources (Trevison et al., 2014, Haque, 2024).

For mixed or open-system scenarios, the teleported energy output typically tracks the population of the dominant eigenstate of the system's steady-state density matrix, establishing a leading-eigenstate rule (Yan et al., 3 Nov 2025).

3. Experimental Realizations and Scalability

QET has been implemented on various physical platforms, including nuclear magnetic resonance (NMR) systems and superconducting quantum hardware (Ikeda, 2023, Ragula et al., 7 May 2025). In the two-qubit minimal model, experimental efficiencies of $M_A(\mu)$0–$M_A(\mu)$1 have been achieved, with the quantum hardware measurements matching theoretical predictions after error mitigation (Ikeda, 2023, Hassan et al., 2024).

Protocols have been extended to multipartite and networked settings. For example, QET via W-state entanglement in three- and five-qubit systems demonstrates decremental energy extraction by multiple receivers, with summed energies never exceeding the sender's input (Khan et al., 3 May 2025). In such architectures, the W-state's resilience to single-site loss maintains energy-extraction capability for the remaining nodes.

Scalability in gapped many-body systems is fundamentally impeded by the exponential decay of quantum correlations with distance, typically limiting long-range QET. However, repeater-inspired architectures employing heralded link generation, purification, and nested swapping convert exponential scaling to polynomial cost, enabling physically tractable QET at arbitrary separation in systems such as the 1D anisotropic XY chain (Abd-Rabbou et al., 26 Jan 2026).

4. Trade-Offs with Quantum Information Teleportation

QET shares the LOCC-and-entanglement structure of quantum information teleportation (QIT), but these two tasks are mutually competitive: both draw on a finite entanglement budget, and any gain in one protocol reduces the other (Wang et al., 2024). Quantitative trade-off relations have been established, e.g.,

$M_A(\mu)$2

where $M_A(\mu)$3 is the entropy transferred (QIT), $M_A(\mu)$4 is the thermodynamic cost of QET, and $M_A(\mu)$5 is the entropy of the resource Gibbs state. Thus, maximal performance in energy versus information teleportation cannot be simultaneously achieved given a fixed entanglement resource.

In holographic setups (AdS$M_A(\mu)$6/SYK traversable wormhole protocols), a first-law-like relation $M_A(\mu)$7 holds perturbatively; in generic finite-dimensional settings, the bound $M_A(\mu)$8 applies (Wang et al., 2024).

5. Synthetic Distance-Dependence and Extensions

In massless quantum field settings, QET mediated by vacuum correlations yields a strict distance suppression, $M_A(\mu)$9, due to quantum energy inequalities (Hotta et al., 2013). However, pre-engineering squeezed local-vacuum regions or employing high-dimensional qudit probes lifts this limitation, allowing for distance-independent or even asymptotically limitless energy transfer—at the expense of injecting additional positive background energy or exchanging large amounts of classical information (Verdon-Akzam et al., 2015, Hotta et al., 2013).

Timelike QET protocols, which exploit both spatial and temporal correlations, can boost energy-extraction efficiency from a few percent (standard QET) to as much as $E_{\text{in}}$0 by letting the disturbance from Alice's measurement evolve prior to Bob's feedback operation and harvesting nontrivial "entanglement in time" (Ikeda, 7 Apr 2025, Twagirayezu, 28 May 2025).

6. Applications in Quantum Thermodynamics, Quantum Networks, and Verification

QET provides both technological and foundational benefits:

• Thermodynamics and algorithmic cooling: QET outperforms standard heat bath algorithmic cooling (HBAC) in strongly interacting qubit systems, enhancing the purity of target subsystems beyond the HBAC limit, through exploitation of system correlations as a cooling resource (Ragula et al., 7 May 2025).
• Quantum key distribution: QET-based QKD protocols are robust to classical and quantum noise, enable dishonest participant detection, and permit one-to-many secret sharing by parallelizing energy-extraction operations conditioned on the sender's broadcast (Dolev et al., 1 Jun 2025).
• Negative-energy state engineering: Field-theoretic QET enables the production of negative average stress-energy densities at prescribed spacetime locations, saturating quantum-inequality scaling bounds and providing new tools for semiclassical gravity experiments (Ragula et al., 7 May 2025).
• Quantum interactive proofs: QET provides completeness and soundness properties for quantum interactive proof protocols, enabling zero-knowledge authentication where only the prover's local qubit measurement outcome needs to be verified (Ikeda et al., 2023).

7. Theoretical Generalizations and Relaxation of Constraints

Recent advancements have shown that QET does not fundamentally require ground-state initialization, commutation between the measurement and interaction terms, or even entanglement. Energy can be extracted via LOCC even from excited or product states, provided measurement-conditioned local effective Hamiltonians are constructed, thereby generalizing the operational applicability of QET (Xie et al., 7 Feb 2025, Haque, 2024). Such protocols enable extraction of locally inaccessible energy locked by strong local passivity, and analytical expressions permit optimization-free determination of the optimal feedback operation.

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The theoretical and experimental development of QET protocols has established them as central constructs bridging concepts in quantum thermodynamics, information theory, and quantum many-body physics. QET underpins concrete advances in energy-efficient quantum technologies, quantum certification, and spacetime engineering, and ongoing research continues to extend its reach in both practical and foundational directions (Khan et al., 3 May 2025, Ikeda, 2023, Haque, 2024, Abd-Rabbou et al., 26 Jan 2026, Wang et al., 2024, Ragula et al., 7 May 2025, Xie et al., 7 Feb 2025).