If entanglement is the vacuum's fuel line, then the cell array has a scaling law

Why the library suggests it

The protocol has been run on superconducting qubits on public machines and on nuclear spins in a molecule, with the energy at the receiving end measured going below the ground-state level in both (Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware, 2023; Experimental Activation of Strong Local Passive States with Quantum Information, 2023).

Try the three shapes the measurement could come back with — delivered energy per cell falling, holding level, or climbing — before the run that decides which one it is.

The quantum-energy-teleportation ledger

Two cells sit in the entangled ground state of a small system. Alice measures hers and her device pays for it, because a ground state can only be raised by a local operation. One classical bit crosses to Bob at no more than light speed, and the operation that bit selects lets his device collect energy that was already sitting beside him as a suppressed fluctuation. Keep the ledger open while you move the model and watch the one thing that never happens: more coming out than went in.

What to look at

The two-cell ledgerEnergy per cell as cells are added. Illustrative — not data

• Delivered per cell
• Spent per cell

Try a trend

Delivered energy per cell falls as cells are added. Illustrative — not dataDelivered energy per cell holds level. Illustrative — not dataDelivered energy per cell climbs. Illustrative — not data

Number of cells

16

Back to the published parameters

Delivered per cell:

0.35

Spent per cell:

2.00

Delivered over spent:

0.18

Illustrative — not data

Drawn shape, not a measurement: no scaling curve for this protocol has been published.

Reading: Illustrative — not data. Number of cells 16. Delivered per cell: 0.35. Spent per cell: 2.00. Delivered over spent: 0.18.

At h of 1.5 and k of 1 on ibmq jakarta, the coupling term at Bob's end reads minus 0.1079 — about 76 per cent of the exact value, and negative on every one of the six IBM machines used. A negative reading there is the whole observation: the local energy has gone below the ground-state level.

The transfer beats the system's own dynamics. Alice reports inside about ten nanoseconds against a coupling time of order a hundred, so Bob has his energy before the chain could have carried any to him.

The independent run used three carbon-13 nuclei in trans-crotonic acid on a 700 megahertz spectrometer at room temperature, and took fourteen milliseconds against a spin-spin coupling of 1.16 hertz — far faster than energy could cross the molecule.

Over a distance, the vacuum-state protocol is capped at one over twelve pi times the separation, because the below-vacuum region at Bob's end has to be propped up by positive energy nearby. Put a squeezed vacuum state in the gap and that support comes from the gap instead, and the falloff goes away.

Run the same machinery in reverse and it puts more energy into one cell than an equal share of the total allows — the storage half of the same architecture.

The protocol has been in the literature since 2008 and has now been run on superconducting qubits and on nuclear spins, with the energy at the receiving end measured going below the ground-state level in both.

The measurement that would settle it: energy delivered per receiving cell and total energy spent per receiving cell, both against the number of cells, on hardware that already exists. The first rung of it costs nothing but a login to a public quantum computer.

The sheets this instrument reads

• Hotta, the spin-chain protocol that started it (2008)
• Hotta, measurement information as the key to local vacuum energy (2008)
• Hotta, the introductory review of the protocol (2011)
• Hotta, Matsumoto and Yusa, the version without a limit of distance (2014)
• Frey and colleagues, the exact limits on local energy extraction (2019)
• Ikeda, the demonstration on superconducting hardware (2023)
• Rodriguez-Briones and colleagues, the nuclear-spin experiment (2023)
• Hotta and Ikeda, the protocol in reverse as a quantum battery (2025)

ibmq lima · ibmq jakarta · ibmq hanoi · ibm cairo · ibm auckland · ibmq montreal · 14 ms · 10 ns

The theoretical boundary of purely local extraction is known exactly, reduced to one operator inequality, along with the ingredient that reopens the door — classical communication between the two regions (Fundamental Limitations to Local Energy Extraction in Quantum Systems, 2019). The distance falloff that kept the protocol millimetre-scale is removed by supplying squeezed vacuum in the gap, which is a resource the field already manufactures routinely (Quantum energy teleportation without a limit of distance, 2014). And the same machinery run in reverse concentrates more energy into a single cell of a quantum battery than the classical ceiling allows (Exceeding the maximum classical energy density in fully charged quantum batteries, 2025), which means the array has a storage mode as well as a transport mode. The authors of the nuclear-spin experiment name the further connection themselves: the same protocol bears on violations of energy conditions in quantum field theory in curved spacetime, which is the exact quantity metric engineering asks for.

The experiment or build

Run the two-qubit protocol at n equals two, then build chains and lattices at four, eight and sixteen, on hardware that already exists. Hold the classical channel cost and the measurement cost in the ledger from the first run. The settling measurement is energy delivered per receiving cell, and total energy spent per receiving cell, both plotted against the number of cells and against the correlation length of the ground state.

If the delivered-energy curve falls more slowly than the cost curve, the architecture has a direction; if it does not, that is a published bound on an idea the field currently only speculates about, and it also feeds directly into the energy-condition question this site's propulsion chapters depend on.