Six months after Australian scientists demonstrated the world’s first working quantum battery prototype, a new theorem published in PRX Quantum establishes that the field’s most celebrated engineering advantage — using quantum entanglement to supercharge battery power — comes with a mathematically inescapable cost: the more entanglement a design exploits, the more its power output fluctuates, with no design workaround possible. The theorem is not a study of specific materials or experimental conditions. It is a proof, derived from the same Heisenberg uncertainty principle that governs the position and momentum of subatomic particles, that every quantum battery ever built or ever to be built faces an irreducible reliability trade-off between how stably it delivers energy and how stably it delivers power. The paper’s core finding was confirmed in the peer-reviewed PRX Quantum publication.

The paper, “Fundamental Limitations on the Reliabilities of Power and Work in Quantum Batteries,” appeared in PRX Quantum 7, 033057 on September 15, 2026, and was selected by the American Physical Society as “Featured in Physics” — a designation reserved for research the APS editors consider significant beyond its immediate field. The four-author team spans Finland, Germany, Spain, and India: Brij Mohan at the University of Oulu’s Nano and Molecular Systems Research Unit; Tanmoy Pandit at VTT Technical Research Centre of Finland, QMill Oy in Espoo, the Leibniz University of Hannover, and TU Berlin; Maciej Lewenstein at ICFO–Institut de Ciències Fotòniques in Barcelona; and Manabendra Nath Bera at IISER Mohali.

Why This Matters Now: World’s First Prototype Changes the Stakes

Understanding fundamental limits on quantum batteries became urgent earlier this year, when CSIRO, Australia’s national science agency, together with teams from RMIT University and the University of Melbourne, published the world’s first quantum battery prototype in March 2026. That device demonstrated a property theorists had long predicted but never observed in hardware: as the battery grows larger, it charges faster, inverting the familiar relationship in conventional batteries where more capacity means more charging time.

“Our findings confirm a fundamental quantum effect that’s completely counterintuitive: quantum batteries charge faster as they get larger. Today’s batteries don’t function like that,” Dr. James Quach, quantum science and technologies science leader at CSIRO who led the prototype team, said in the CSIRO announcement.

But the same collective quantum behavior — the entanglement of molecules acting in unison during charging — that produces this speed advantage is precisely what the Mohan et al. theorem identifies as the source of reliability degradation. The CSIRO prototype demonstrated the power advantage experimentally. The PRX Quantum paper now proves that any design replicating that advantage, at any scale, will simultaneously face power fluctuations that grow faster than average power itself.

What Is a Quantum Battery?

Unlike the lithium-ion cells powering today’s smartphones and electric vehicles, a quantum battery stores energy not in chemical bonds but in discrete quantum states of microscopic physical systems — such as the spin states of individual atoms or the excited states of molecules confined in an optical cavity. The battery is charged by an external field that drives transitions between these states; the maximum energy extractable through a reversible (unitary) process is called ergotropy, a term Alicki and Fannes 2013 formalized.

The concept dates to a 2013 paper by Robert Alicki and Mark Fannes, who showed theoretically that quantum entanglement could boost extractable work from an ensemble of quantum cells. Subsequent research established that collective charging — where all cells in a many-cell battery interact and entangle during charging — can dramatically increase average charging power compared with charging each cell independently in parallel.

Quantum batteries are not a commercial product. As of 2026, they exist only as tabletop proof-of-concept devices, with the CSIRO-led prototype representing the state of the art. Their primary proposed application is as on-chip power sources for quantum processors, sensors, and communication nodes — settings where conventional electrical noise would disrupt the delicate quantum states that make quantum computing work. A 2024 colloquium in Reviews of Modern Physics surveys quantum battery research comprehensively up to that date.

How Reliability Is Measured: Noise-to-Signal Ratio

To quantify reliability, the paper uses a quantity physicists call the noise-to-signal ratio, or NSR: the variance in a measured quantity divided by the square of its average. A battery that delivers exactly the same amount of work every time has a work NSR of zero — perfect reliability. One whose output fluctuates has a high NSR and would be unpredictable.

The same concept applies to power — the rate at which energy is delivered. A quantum processor requires not just a fixed total energy supply but a stable, predictable power stream. High fluctuations in either quantity degrade performance in qualitatively different ways: work fluctuations mean the battery might deliver too much or too little total energy; power fluctuations mean it might deliver the energy too fast or too slow, disrupting the timing of quantum gate operations.

The Theorem: Non-Commuting Operators and an Inescapable Trade-Off

The paper’s central finding emerges from a structural property of quantum mechanics. The work deposited in a quantum battery is represented mathematically by the battery’s internal Hamiltonian, H₀ᴮ. The instantaneous power is represented by the commutator of H₀ᴮ with the external charging Hamiltonian Hᵗᶜ — specifically, the operator P₀ = −(i/ℏ)[H₀ᴮ, Hᵗᶜ]. The full mathematical derivation appears in the paper’s appendices.

These two operators — the work operator and the power operator — do not commute with each other for any non-trivial charging protocol. Non-commutativity is the condition that triggers the Robertson-Schrödinger uncertainty relation, the generalized version of Heisenberg’s principle. The original Heisenberg uncertainty principle says that precise simultaneous knowledge of a particle’s position and momentum is impossible; the Robertson-Schrödinger form (derived independently by Howard Percy Robertson in 1929 and Erwin Schrödinger in 1930) extends this to any pair of non-commuting quantum observables whatsoever. The Robertson 1929 derivation is the foundational reference the paper builds on.

When the team applied the Robertson-Schrödinger relation to the normalized work and power operators, they obtained the fundamental trade-off (Equation 6 in the paper):

NSR(work) × NSR(power) ≥ ¼|⟨[P̃, W̃]⟩|² + ¼|⟨{P̃, W̃}⟩ − 2|²

The right-hand side is always non-negative and, in general, non-zero. This means the product of the two NSRs — the product of the two instabilities — has a floor that cannot be driven to zero simultaneously for both. The paper’s Equations 6, 8, and 9 establish this result.

In plain terms: any charging protocol that suppresses power fluctuations will, by mathematical necessity, allow energy fluctuations to grow, and vice versa. The trade-off is not a property of any specific battery design, material, or size. It is a theorem.

“A quantum battery ideally should not only be fast and powerful but also needs to charge or deliver energy in a reliable and stable manner at the same time,” said Brij Mohan, postdoctoral researcher at the University of Oulu and the paper’s lead author, in remarks quoted in the study. “Our work shows that quantum mechanics places fundamental limits on the reliabilities of quantum batteries.”

The Entanglement Trap: Cubic Fluctuations vs. Linear Power Gain

The paper’s most immediately practical finding concerns many-body quantum batteries — systems with multiple cells charged collectively. Prior research established that collective charging using entanglement boosts average power. The Mohan et al. analysis agrees, but exposes the hidden cost.

In the paradigmatic model studied (N spin-½ particles charged with k-body interactions), average power scales linearly with the interaction strength k. But power fluctuations grow as k³ — cubically. The NSR of power, which measures instability, is proportional to k/N, and for fully collective charging (k = N), the product of work and power NSRs equals exactly 1 — the worst possible regime for reliability. The full scaling analysis covers both paradigmatic and Ising-chain models.

Conversely, collective charging (larger k) actually improves work reliability — the NSR of work decreases toward collective charging. The two reliability metrics move in opposite directions as entanglement increases. Parallel charging (k = 1) optimizes power reliability at the expense of work reliability and raw power; collective charging does the reverse.

“Quantum batteries offer a fascinating link between quantum information, thermodynamics, and many-body physics,” said co-author Maciej Lewenstein, ICREA Research Professor at ICFO in Barcelona, in Lewenstein’s remarks in the paper. “Understanding their fluctuations is essential if these systems are eventually to become useful technological resources.”

The team confirmed the same qualitative trade-off in a second model family: transverse-field Ising chains with s-body interactions (s = 2, 3, and 4 tested). Longer-range interactions boosted average power but drove up power fluctuations, while work reliability improved. The agreement between the two model families — a generic spin-½ many-body battery and an experimentally motivated Ising model — strongly suggests the trade-off is a universal feature of quantum battery physics rather than an artifact of any particular system.

What Builders Can Actually Do: Universal Cluster Scaling

The paper does not simply identify a wall — it provides the scaling law that tells designers exactly where to find the best achievable compromise.

For a hybrid charging strategy — one that groups the battery’s N cells into clusters of size k and charges each cluster collectively, while charging different clusters in parallel — the product of the work and power NSRs obeys a clean formula regardless of time:

NSR(work) × NSR(power) = k²/N²

The team calls this “universal cluster scaling.” It is time-independent, which means it characterizes the fundamental reliability budget of any hybrid design, regardless of when during the charging cycle the measurement is taken. The universal cluster scaling derivation appears in Equation 9 of the paper.

For a designer, this formula gives a direct quantitative lever. A battery with 100 cells (N = 100) and clusters of 10 (k = 10) has a reliability-product floor of 100/10,000 = 0.01. Fully collective charging (k = N = 100) gives a floor of 1 — one hundred times worse. Fully parallel (k = 1) gives a floor of 0.0001 — the best reliability, but at the cost of no entanglement-assisted power advantage.

The optimal k for any application is the one that balances the engineering requirements for power output (which improves with larger k) against the requirements for energy and power stability (which improve with smaller k). The formula tells designers exactly what that trade-off costs for any chosen cluster size.

“Our results show that there is a meaningful way to balance power enhancement and the reliability of work and power,” said co-author Tanmoy Pandit of VTT Technical Research Centre of Finland, QMill Oy, and collaborating German institutions, in co-author remarks within the paper. “Intermediate-range interactions based charging scheme can provide a useful compromise between high power and stable operation.”

What the Paper Does Not Cover

The theorem is explicitly restricted to closed, noiseless quantum systems — idealized models in which the battery is perfectly isolated from its environment. Real quantum devices are never perfectly isolated. Decoherence, thermal noise, and energy leakage to the environment are the dominant engineering challenges confronting every experimental quantum system, including the CSIRO prototype, which currently stores energy for only nanoseconds before it dissipates.

The authors identify extending the framework to open quantum systems — ones that interact with an environment — as the natural next step for the theory. Real-world noise is expected to introduce additional trade-offs beyond those established here. The closed-system result thus represents a theoretical floor: real quantum batteries will face at least these reliability constraints, and likely additional ones imposed by dissipation.

Photonic quantum batteries and experimentally accessible platforms are also identified as directions for follow-on work. The paper’s framework uses full counting statistics (FCS) to compute averages and fluctuations, a formalism that correctly handles quantum coherence in the initial battery state — an improvement over the simpler two-point measurement protocol that can miss coherence-dependent effects. The full technical framework is developed in the paper’s appendices.

What Engineers Building Quantum Power Supplies Now Need to Know

For the engineers and researchers designing on-chip power supplies for quantum processors and sensors — the practical application motivating most quantum battery research — the paper delivers three actionable conclusions.

First: claiming both high power output and high stability simultaneously is not a matter of insufficient engineering ingenuity. It is physically impossible. Any design that achieves unusually high entanglement-assisted power is, by the theorem, also delivering unusually unreliable power — meaning the fluctuations in its power output will be proportionally large. This is a permanent feature of the physics, not a current-generation limitation to be solved with better materials or fabrication.

Second: the work reliability and power reliability of any many-body quantum battery move in opposite directions as entanglement increases. Designers must decide which metric their application is more sensitive to and optimize accordingly. A quantum processor gate timing system is sensitive to power fluctuations; a quantum sensor drawing a fixed total energy budget is sensitive to work (energy) fluctuations. The trade-off is not symmetric in its engineering consequences.

Third: the universal cluster scaling law (k²/N²) gives a concrete formula for finding the optimal intermediate design point. Intermediate-range interactions — not fully collective, not fully parallel — are the best available engineering path, and the product of NSRs for any such design is determined entirely by the ratio k/N. The Research Council of Finland and the European Union’s Horizon Program, which funded portions of this research, will likely see follow-on experimental work testing whether the hybrid cluster approach performs as predicted in physical systems.

Frequently Asked Questions

What is a quantum battery, and why is it different from a regular battery?

A quantum battery stores energy in discrete quantum states of subatomic-scale systems — the spin of atoms or the excited states of molecules — rather than in chemical bonds. The key difference is that quantum batteries can exploit superposition and entanglement to charge faster and potentially store more energy per unit volume than any chemistry-based alternative. The concept was first proposed theoretically in 2013, and the world’s first working proof-of-concept prototype was demonstrated in March 2026 by CSIRO, RMIT University, and the University of Melbourne. However, fully practical quantum batteries do not yet exist, and the current prototype stores energy for only nanoseconds.

What exactly does the uncertainty principle have to do with battery reliability?

The Heisenberg uncertainty principle — in its general Robertson-Schrödinger form — states that any two quantum observables represented by non-commuting operators cannot both be made arbitrarily precise simultaneously. In a quantum battery, the total energy deposited (work) and the rate of energy deposition (power) are represented by exactly such non-commuting operators. The Mohan et al. 2026 paper proves formally that this non-commutativity means no charging protocol can simultaneously suppress fluctuations in both work and power. It is the same class of mathematical constraint that prevents a physicist from knowing a particle’s position and momentum with perfect precision at the same time — now applied to battery engineering.

If I’m building a quantum battery, how do I choose between power and energy stability?

The paper provides a quantitative answer through universal cluster scaling. For a battery with N total cells using hybrid charging with cluster size k, the product of the work and power noise-to-signal ratios equals k²/N². This formula is time-independent, so it characterizes the system’s fundamental reliability budget regardless of where in the charging cycle you measure. Larger clusters (larger k) mean more entanglement-assisted power but worse power reliability; smaller clusters mean better power reliability but less raw power advantage. The specific application determines which trade-off is acceptable: gate-timing-sensitive quantum processors need power stability; fixed-energy-budget systems need work stability. Choosing an intermediate k — neither fully collective nor fully parallel — is the engineering optimum that the paper formally recommends.

Does this theorem mean quantum batteries will never work?

No. It means quantum batteries face fundamental constraints on simultaneous reliability of power and energy delivery that no design can eliminate — but it also provides the engineering path to the best achievable compromise. The constraint is analogous to the Carnot efficiency limit on classical heat engines: it does not prevent engines from working; it tells designers what maximum efficiency is possible and how to approach it. The paper’s hybrid cluster scaling law gives quantum battery designers a concrete formula for navigating the trade-off. The CSIRO 2026 prototype already demonstrated that the power advantage is real. The theorem tells researchers what price must be paid for that advantage and how to minimize it.