Quantum Energy Teleportation

Quantum energy teleportation (QET) is a correlation-assisted local-energy extraction protocol. A measurement in region $A$ injects energy and produces a classical outcome; after that outcome reaches region $B$, a conditional local operation can extract energy there. No energy or information propagates outside the light cone, and “teleportation” does not mean that the extracted energy traveled from $A$ to $B$.

Required background. Passivity and work fixes the energy reference, measurement energy and backreaction supplies the instrument account, and quantum energy inequalities constrain regulated local energy profiles.

Helpful background. Entanglement harvesting distinguishes use of pre-existing correlations from causal energy exchange.

Measurement, message, and extraction

Let $\{M_a\}$ be a localized instrument in $A$, with outcome probability $p_a$, and let $U_a^B$ be a local unitary in $B$ chosen after receiving $a$. The averaged final state is

$$\rho_f=\sum_a U_a^B M_a\rho_0 M_a^\dagger U_a^{B\dagger}.$$

With a fixed Hamiltonian $H$, define measurement injection

$$E_A=\sum_a\operatorname{tr}(H M_a\rho_0M_a^\dagger) -\operatorname{tr}(H\rho_0)$$

and remote extraction

$$E_B=\sum_a\operatorname{tr}\!\left[ H\left(M_a\rho_0M_a^\dagger- U_a^B M_a\rho_0M_a^\dagger U_a^{B\dagger}\right) \right].$$

A successful protocol has $E_B>0$ while respecting the causal delay for the classical message. Local passivity can forbid extraction by an outcome-independent operation at $B$ even though correlations make the conditioned operation effective. Hotta 2010, §§ 2–4 develops this mechanism in regulated spin and field models.

A regulated field-chain test

Start with a finite harmonic chain approximating a scalar field ground state. Choose separated blocks $A$ and $B$, a finite-resolution Gaussian measurement in $A$, and an outcome-dependent displacement in $B$. Optimize $U_a^B$ using the conditional first moments and covariance. Report:

• $E_A$, $E_B$, controller and message costs;
• the separation and earliest allowed feed-forward time;
• the result with the $A$–$B$ covariance set to zero;
• lattice-spacing, volume, and measurement-resolution convergence.

If the message is removed, average over an outcome-independent $U^B$ and verify that the claimed extraction disappears. If the initial correlations are removed while local marginals are matched, the advantage should disappear. These are stronger causal controls than observing $E_B>0$ once.

QET joins the localized-instrument branch to passivity and a complete energy account. The relevant resource is the conditional correlation structure; the classical message controls a local extraction operation. The diagram is schematic.

Causal and energetic interpretation

Before the message reaches $B$, the reduced statistics of every operation in $B$ are independent of $a$. The final local negative-energy region is balanced by the measurement injection, subsequent propagation, and positive energy elsewhere according to the model’s dynamics and applicable energy inequalities. Correlation alone is not sufficient: the instrument and conditional operation must couple to it in the right way.

Calling the protocol superluminal, identifying correlation with transported energy, or omitting measurement injection and feed-forward cost are distinct errors. The map is schematic.

Evidence boundary

As of 10 August 2026, QET has rigorous and numerical realizations in finite spin, oscillator, and field-theory models. Quantum processors have executed circuits representing small QET Hamiltonians, including Ikeda 2023, “Superconducting Quantum Hardware,” §§ II–IV, and field-theory simulations have explored critical enhancement in the massive Thirring model Ikeda 2023, “Criticality,” §§ II–IV. These results do not yet demonstrate spatially separated continuum-field energy extraction in a laboratory; hardware simulation of a model and direct measurement of a field protocol are different evidence classes.

References

• Hotta, Masahiro. “Quantum Energy Teleportation: An Introductory Review.” Journal of Physics A: Mathematical and Theoretical 43 (2010): 105305. DOI.
• Ikeda, Kazuki. “Criticality of Quantum Energy Teleportation at Phase Transition Points in Quantum Field Theory.” Physical Review D 107 (2023): L071502. DOI.
• Ikeda, Kazuki. “Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware.” Physical Review Applied 20 (2023): 024051. DOI.