The quantum-energy-teleportation cell

Why the library suggests it

Hold on to the accounting: the measurement pays, the wire carries only the result, and the far end can collect no more than was paid. Move the model and watch where the far end stops.

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

• Paid in at the measurement
• Ceiling: never more than was paid in

Reading

Model parameter h

1.5

Model parameter k

1.0

Back to the published parameters

Paid in at the measurement:

1.25

One classical bit crosses:

1

Ceiling: never more than was paid in:

1.25

Delivered over spent:

1.00

Reading: Paid in at the measurement: 1.25 in the model's energy unit. One classical bit crosses. Ceiling: never more than was paid in: 1.25.

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

Masahiro Hotta's protocol moves energy out of a patch of field that has none, using a measurement here, a classical message, and a conditioned operation there (Quantum measurement information as a key to energy extraction from local vacuums, 2008). Kazuki Ikeda ran it on six IBM machines, one of them free to the public, and measured the local energy going below the ground-state level (Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware, 2023). Nayeli Rodríguez-Briones and colleagues did it on three carbon nuclei in a crotonic-acid molecule in fourteen milliseconds, far faster than energy could have crossed the molecule (Experimental Activation of Strong Local Passive States with Quantum Information, 2023). The exact boundary of what purely local operations can do — and the fact that classical messages reopen the door — is drawn in Fundamental Limitations to Local Energy Extraction in Quantum Systems (2019), and the distance limit that kept the protocol millimetre-scale is removed by putting squeezed vacuum in the gap (Quantum energy teleportation without a limit of distance, 2014).

The experiment or build

Start on a public quantum computer: the circuit is six gates deep and free to run. Then build the physical version — a chain of superconducting qubits, or the nuclear magnetic resonance version on a benchtop spectrometer — and turn it into an engineering question rather than a demonstration: put many cells in parallel, measure the energy delivered per cell, and measure the total energy spent on measurement, control and the classical channel. The settling measurement is the ratio of energy delivered at the receiving end to total energy spent across the whole apparatus, as a function of the number of cells. Nobody expects that ratio to pass one; what nobody has published is how it scales, and the scaling is the entire engineering question. A companion result shows the same protocol run in reverse puts more energy into one cell of a quantum battery than the classical share allows (Exceeding the maximum classical energy density in fully charged quantum batteries, 2025), which is the storage half of the same architecture.