Historical research guide · 1042 · 2025

Exceeding the maximum classical energy density in fully charged quantum batteries

Masahiro Hotta · Kazuki Ikeda

In one minute

Masahiro Hotta and Kazuki Ikeda take a rule that looks unbreakable and break it. Charge an ordinary battery as full as it will go and each of its cells holds at most the total divided by the number of cells. That is the classical ceiling on energy density. Hotta and Ikeda show that a battery made of entangled qubits can put more than that share into a single cell, and they show exactly how. Their protocol is Hotta’s own quantum energy teleportation run upside down: instead of starting from the ground state, start from the highest energy state, which is the ground state of the same Hamiltonian with its sign flipped. Alice measures her qubit — which draws energy out at her end and, because her measurement commutes with Bob’s local Hamiltonian, changes nothing at his — and sends him one classical bit. Bob applies a rotation conditioned on that bit, and his cell now carries energy that no unitary operation could have given him. The entanglement in the top state is what pays.

Connection

Chapter 6 is about drawing usable energy out of a field rather than burning fuel, and this is that accounting made concrete and hardware-ready: entanglement in a many-body state is a resource that a local measurement plus one classical bit converts into local energy someone can take out and use. Chapter 2 gets the sharper point — the energy sitting at one place is not fixed by the global state alone, which is precisely the structure this site argues the vacuum has.

From the source

In a classical battery the energy density at each subsystem is capped at the maximum stored energy divided by the number of subsystems. Hotta and Ikeda demonstrate that a quantum battery running a quantum energy teleportation protocol surpasses that cap, so one subsystem can hold more than its classical share and that surplus can be extracted from it directly.Abstract, and Section III with Figure 2 (arXiv:2407.01832v2)
The protocol is quantum energy teleportation turned upside down. Instead of the ground state it uses the highest energy state of the Hamiltonian, which is the ground state of the same Hamiltonian with its sign reversed. The authors summarise their whole proposal in one line: quantum energy teleportation for the maximum-energy state is a quantum battery.Section I, closing paragraphs, and Section III, opening (arXiv:2407.01832v2)
The mechanics are local measurement plus one classical bit. Alice measures a Pauli operator on her qubit and draws energy out at her end; because that measurement commutes with Bob’s local Hamiltonian it leaves his local energy untouched. She sends him the single-bit outcome, he applies a rotation conditioned on it, and the paper proves his resulting local energy is not smaller than what he started with.Section III, equations 2 and 3, and the optimised operation in equations 4 to 7 (arXiv:2407.01832v2)
No unitary operation could do this. In the minimal two-qubit model the maximum-energy state has zero expectation for the total Hamiltonian, for each local Hamiltonian and for the interaction term alike, so Bob waiting or acting on his own can never rise above zero. Alice’s measurement is what breaks unitarity, and after it his local energy is strictly positive.Section IV, equations 9 and 10, the paragraph following equation 10, and equation 13 (arXiv:2407.01832v2)
The mechanism is generic rather than a feature of one design: the interaction term between subsystems enhances local energy fluctuations, in the same way that quantum energy teleportation drives a region below the ambient vacuum level. Entanglement surviving in the highest energy eigenstate is what makes the surplus available.Section III, the paragraph on the mechanism, with Figure 1 (arXiv:2407.01832v2)
The hard half is already built. The quantum energy teleportation step has been run on superconducting quantum hardware and in trapped-ion and nuclear-magnetic-resonance experiments, the authors publish their implementation code, and charging through local operations and classical communication is instantaneous — which is why they argue this route to a working quantum battery is less cumbersome than the alternatives.Section III, the paragraph before Section IV; Section IV, opening; and the implementation repository cited as reference 28 (arXiv:2407.01832v2)

The way in

https://doi.org/10.1007/s11128-025-04804-8

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

LICENCE CHECKED, NOT CC BY. Many Quantum Information Processing papers are Creative Commons, so this one was checked directly rather than assumed. Crossref returns two licence entries for this DOI and both point at the Springer Nature text-and-data-mining terms, one for the accepted version and one for the version of record; no Creative Commons statement is attached. OpenAlex records the publisher location with a null licence and an open-access status of green, meaning the only free copy is the author copy in a repository. The Springer landing page could not be retrieved directly, since link.springer.com returns a stub to automated requests. On that evidence the published article stays abstract-only. SOURCE READ. The authors’ preprint, arXiv:2407.01832v2 dated 24 June 2025, was downloaded and read in full for this page, and the locators below cite its section, equation and figure numbers. It carries the arXiv non-exclusive distribution licence, which is not a Creative Commons licence. ABSTRACT REPRODUCED. The abstract below is the published Springer abstract, in which the mathematical symbol for the classical maximum energy density is set as E with subscript C; it is written EC in plain text here, exactly as the fetched text renders it. PUBLICATION DETAILS: Quantum Information Processing volume 24, issue 6, article number 186, published 18 June 2025. AUTHOR AFFILIATIONS as printed: Masahiro Hotta, Department of Physics, Tohoku University, Sendai, and the Leung Center for Cosmology and Particle Astrophysics, National Taiwan University; Kazuki Ikeda, Department of Physics, University of Massachusetts Boston, the Center for Nuclear Theory at Stony Brook University, and the Co-design Center for Quantum Advantage. RELATED PAGES on this site: Hotta’s introductory review of quantum energy teleportation at /library/stm-5aa6b8b006, the spin-chain protocol at /library/stm-570318f99e, the local-vacuum extraction paper at /library/stm-e7e45ffaae, the long-distance version at /library/stm-2e579e12bc, Ikeda’s demonstration on superconducting hardware at /library/stm-6f13e92d8b, the nuclear-magnetic-resonance activation experiment at /library/stm-059e4a4536, the limits paper at /library/stm-53ea17cc58, and Hotta, Schützhold and Unruh on partner particles at /library/stm-a0c0727ca5.

How to cite it

Masahiro Hotta, Kazuki Ikeda (2025) Exceeding the maximum classical energy density in fully charged quantum batteries doi:10.1007/s11128-025-04804-8

Where it sits in the curriculum

Energy from the vacuum