A No-Go Theorem for Measurement-Powered Quantum Heat Engines

Quantum thermodynamics is full of tempting phrases: engines powered by measurement, Maxwell demons that convert information into work, cooling “beyond Carnot,” and machines whose fuel is not a hot flame but quantum backaction. A new preprint by Kenta Koshihara and Kazuya Yuasa of Waseda University adds an important constraint to that conversation. Their paper, “No-Go Theorem for Quantum Heat Engines Powered Purely by Quantum Measurements in the Steady Regime” (arXiv:2604.22376, submitted April 24, 2026), asks whether a finite-dimensional quantum engine can keep producing work if its only energy source is repeated bare quantum measurement.

The answer is deliberately conservative: not in the steady regime. If there is no feedback control, no thermal contact, and no hidden entropy-lowering operation in the cycle, then bare measurements eventually become nondisturbing. They stop injecting energy into the working substance, and the engine cannot extract work.

The result is not an attack on quantum engines. It is a boundary marker: measurement backaction can be a resource only when the full thermodynamic bookkeeping includes the entropy sink that makes the resource usable.

Why measurement looked like a possible fuel

In ordinary thermodynamics, a heat engine draws energy from a hot reservoir, rejects waste heat to a cold reservoir, and converts part of the difference into work. Quantum measurement changes the picture because observing a quantum system is not passive. If a measurement is performed in a basis that does not commute with the system’s energy, it can disturb the state and change the system’s average energy. That disturbance is called measurement backaction.

Over the past decade, researchers have explored whether that backaction can be used the way a hot bath is used in a classical engine. The lineage is real. Maxwell’s demon and information thermodynamics showed that acquired information can be converted into work when feedback is included; reviews by Maruyama, Nori and Vedral, by Parrondo, Horowitz and Sagawa, and by Goold and colleagues helped establish that information has thermodynamic value. In the quantum setting, Elouard and collaborators formulated the stochastic thermodynamics of quantum measurement and demonstrated how measurement backaction could power Maxwell-demon-like engines. Experiments such as Wang et al.’s 2022 two-qubit engine driven by entanglement and local measurements made the idea more than metaphor.

But there is a subtle trap. A general quantum measurement can be operationally equivalent to measuring and then applying an outcome-dependent unitary operation. That is feedback control in disguise. If the goal is to know whether measurement itself can be the fuel, the measurement must be stripped down to a bare operation: no conditioned correction, no selected outcome, no thermal reset, no information-powered controller secretly doing the work.

The engine the paper rules out

The authors consider a finite-dimensional working substance. A cycle contains repeated steps: perform a bare quantum measurement, then drive the Hamiltonian by an external unitary operation that does not depend on the measurement outcome. After a fixed sequence of such steps, the Hamiltonian is returned to its initial form so that the device is a cycle rather than a one-off state transformation.

That setup sounds like a minimalist quantum heat engine. There is an apparent energy source, because measurement backaction can change the system’s energy. There is work extraction, because changing the Hamiltonian with external control can exchange work with the apparatus. There is repetition, because an engine should operate cycle after cycle. What is missing is precisely what makes the result sharp: there is no feedback controller and no hot or cold bath in the thermodynamic cycle.

The proof turns on entropy. Bare quantum measurements in this setting are unital quantum operations, and the paper shows that their genuine backaction cannot decrease the entropy of the measured system. In a steady cycle, however, the engine cannot accumulate entropy indefinitely. The total entropy change over a recurring cycle must vanish. If every bare measurement is entropy non-decreasing and the full steady cycle returns to itself, then each measurement must in fact preserve entropy. And if a bare measurement preserves entropy under the conditions identified in the proof, it becomes nondisturbing for the relevant state.

No disturbance means no injected measurement energy. No injected energy means no work extracted from measurement backaction. The engine has lost its fuel.

The recurrence idea in plain language

Koshihara and Yuasa use a Poincaré-like recurrence theorem for general quantum channels. The mathematical language involves completely positive trace-preserving maps, peripheral eigenspaces, and asymptotic dynamics. The plain-language picture is simpler: if the same finite-dimensional quantum process is repeated again and again, the long-time behavior settles into a steady pattern. It may be a fixed point or a limit cycle, but it does not wander forever into fresh thermodynamic territory.

That matters because a one-shot measurement can certainly disturb a system. If you prepare a delicate quantum state and measure it in the “wrong” basis, energy may be injected or removed. But a practical engine must operate repeatedly. Once the repeated measurement-and-driving map reaches its steady regime, the state being measured is no longer a fresh resource. The measurement has become compatible with the steady state. It is no longer doing useful energetic violence to the system.

A one-time kick is not an engine. A repeated machine needs a reset mechanism, a feedback loop, a reservoir, or some other entropy account that balances the cycle.

Why this does not kill measurement engines

The no-go theorem is narrow in the useful scientific sense. It rules out engines powered purely by bare quantum measurements in the steady regime for finite-dimensional working substances. It does not say that quantum measurement can never help produce work. In fact, the paper explains why two established families of measurement-powered engines can work.

1. Feedback-assisted engines

In a feedback-assisted measurement engine, the measurement outcome is recorded and used to choose a later operation. That is the Maxwell-demon route. The demon’s memory, controller, and erasure costs are not optional decorations; they are part of the thermodynamic machine. Work extraction becomes possible because feedback can reduce the entropy of the working substance conditionally, creating room for measurement backaction to increase entropy while the full accounting remains consistent with the second law.

2. Thermalization-assisted engines

In a thermalization-assisted measurement engine, the working substance contacts a thermal reservoir. The measurement may play the role of an effective hot bath, while the ordinary reservoir absorbs heat or resets the state. Work can be extracted because the bath supplies the entropy-balancing process. This is the logic behind single-temperature measurement engines without feedback control, such as the proposal by Yi, Talkner and Kim and later measurement-driven engine studies.

The distinction is crucial for “beyond-Carnot” discussions. Some quantum refrigerators or measurement-assisted devices can appear to exceed classical-looking bounds when one ignores the resource cost of measurement, feedback, squeezing, coherence preparation, or reset. Once those costs are included, the second law is not overthrown. Instead, it is generalized to include the actual resource that the machine consumes.

Where Floquet thinking enters

The paper is not a Floquet-materials experiment, but it is highly relevant to Floquet energy science because the engine is a repeated driven cycle. Floquet engineering is the study of systems controlled by periodic operations: light pulses, microwave modulation, lattice shaking, kicked Hamiltonians, or stroboscopic measurement sequences. In quantum energy devices, the dream is to use the drive’s timing to sculpt energy flow, stabilize useful states, or open channels that are closed in equilibrium.

The no-go result says that periodicity alone is not enough. A repeating quantum operation can produce beautiful transient dynamics, but a steady engine needs a thermodynamic asymmetry. In Floquet language, the stroboscopic map must be coupled to a real resource: a nonequilibrium bath, feedback, reservoir engineering, population inversion, chemical work, coherent pumping, or a carefully accounted measurement apparatus. Otherwise the repeated map relaxes into a regime where bare measurement has no fuel left to provide.

This is especially important for quantum batteries and driven heat engines. Many proposals use periodic driving to charge, stabilize, or extract energy from small systems. The useful question is not “does the drive inject energy?” It is “what resource pays for the injected energy, how much entropy is produced, and what remains after many cycles?” Koshihara and Yuasa’s theorem gives researchers a compact diagnostic: if a proposed machine relies on measurement backaction alone, ask where the entropy decreases.

What researchers should take from the theorem

The strategic value of a no-go theorem is that it narrows the design space. It prevents future papers from accidentally selling a hidden feedback engine as a pure measurement engine. It also pushes the field toward more honest, more useful devices. A measurement-assisted engine can still be valuable if the feedback is fast, the reservoir is engineered, or the measurement apparatus is integrated efficiently. But those pieces must be designed and costed, not waved away.

For experimentalists, the theorem suggests concrete checks. Does the protocol retain outcomes? Is there postselection? Is a controller applying outcome-dependent pulses? Is a thermal bath resetting the working substance? Is the measurement apparatus itself being pumped, cooled, or erased? If yes, the machine may still be a legitimate quantum engine, but the “fuel” is the full information-and-control stack rather than bare measurement alone.

For non-specialists, the message is even simpler. Quantum measurement is weird, powerful, and physically real. It can disturb a system and shift energy. But weirdness is not a loophole in thermodynamics. To turn disturbance into repeatable work, a machine needs a way to export entropy or use information. The 2026 no-go theorem puts that statement on rigorous footing for steady measurement-powered engines.

The bottom line

This is a useful corrective paper for quantum energy research. It does not make quantum heat engines less exciting. It makes them more disciplined. The most promising future devices will probably combine several resources: periodic driving, engineered reservoirs, measurement, feedback, coherence, and many-body structure. But each ingredient has a cost. If a measurement-powered engine claims repeatable work without feedback or thermal contact, Koshihara and Yuasa now provide a strong reason to be skeptical.

That skepticism is productive. The path to useful quantum energy technology will not come from pretending to beat the second law. It will come from identifying exactly which quantum resources are being spent, designing cycles that spend them efficiently, and building experiments where every watt, bit, qubit, and entropy flow is visible.