arxiv: 2604.22376 · v1 · submitted 2026-04-24 · 🪐 quant-ph · cond-mat.stat-mech

Recognition: unknown

No-Go Theorem for Quantum Heat Engines Powered Purely by Quantum Measurements in the Steady Regime

Kenta Koshihara , Kazuya Yuasa

Authors on Pith no claims yet

Pith reviewed 2026-05-08 11:52 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech

keywords quantum thermodynamicsmeasurement-powered enginesno-go theoremsquantum channelssteady stateswork extractionmeasurement backaction

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The pith

Quantum engines powered only by measurements cannot extract work once they reach steady operation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that a finite-dimensional quantum engine driven solely by repeated bare measurements, without feedback or thermal contact, cannot extract net work in the steady regime. It applies a Poincaré-like recurrence theorem to quantum channels to show that the system eventually reaches a fixed point where each measurement becomes nondisturbing and supplies no energy input. A reader would care because this identifies why pure measurement driving fails for steady cycles and why an entropy-reducing step must be added. The result applies to any such engine that settles into repeated identical operations.

Core claim

On the basis of a Poincaré-like recurrence theorem for general quantum channels, we prove a no-go result for work extraction from such an engine in the steady regime. In the steady regime, quantum measurements become nondisturbing and do not inject energy into the working substance. Consequently, no work can be extracted. This result reveals the necessity of an entropy-decreasing process, such as feedback control or thermal contact, for work extraction in steady-cycle measurement-powered engines.

What carries the argument

The Poincaré-like recurrence theorem for general quantum channels, which shows that repeated measurements drive the system to a fixed point at which backaction and energy injection both vanish.

If this is right

No net work can be extracted in the steady regime without an added entropy-decreasing mechanism.
Bare measurements cease to inject energy once the quantum channel reaches its fixed point.
Any steady-cycle measurement-powered engine requires feedback control or thermal contact to produce work.
The no-go holds for arbitrary finite-dimensional working substances under pure measurement driving.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Work extraction might still occur during the transient approach to steady state before the fixed point is reached.
The same recurrence argument could rule out work extraction in other steady quantum thermodynamic cycles that lack an entropy sink.
An experiment could monitor the long-time energy input from measurements on a trapped ion or superconducting qubit to check whether it drops to zero.

Load-bearing premise

The engine truly reaches and stays in a steady regime under repeated bare measurements alone, so the describing quantum channel attains a fixed point where backaction disappears.

What would settle it

Demonstrating sustained positive net work output over many full cycles from a finite-dimensional system driven only by bare measurements that have settled into a steady state without feedback or thermal contact.

Figures

Figures reproduced from arXiv: 2604.22376 by Kazuya Yuasa, Kenta Koshihara.

**Figure 1.** Figure 1: FIG. 1. Quantum measurement-powered heat engines. (a) Feedback-assisted measurement-powered engine [12]. A quantum view at source ↗

**Figure 2.** Figure 2: FIG. 2. The cycle (2.1) of a quantum engine powered view at source ↗

read the original abstract

We study the thermodynamics of a quantum measurement-powered engine that converts energy injected by measurement backaction into work. We consider an engine with a finite-dimensional working substance, driven purely by quantum measurements, i.e., by bare quantum measurements, without feedback control or thermal contact in the thermodynamic cycle. On the basis of a Poincar\'e-like recurrence theorem for general quantum channels, we prove a no-go result for work extraction from such an engine in the steady regime. In the steady regime, quantum measurements become nondisturbing and do not inject energy into the working substance. Consequently, no work can be extracted. This result reveals the necessity of an entropy-decreasing process, such as feedback control or thermal contact, for work extraction in steady-cycle measurement-powered engines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Pure measurement engines can't extract steady work because measurements stop disturbing the system at the fixed point.

read the letter

The one or two things your colleague should know: this paper proves that a quantum engine powered purely by bare measurements cannot extract work once it reaches the steady regime. The measurements stop injecting energy because the system settles into a fixed point of the channel. They apply a Poincaré-like recurrence theorem for quantum channels to this setting, showing that repeated measurements on a finite-dimensional system lead to a state invariant under the measurement, with zero net energy change. This is new for the steady regime of these engines and does well in making the case that an entropy-decreasing process is required for any work output. The paper lays out its assumptions plainly—no feedback, no thermal baths, cycle of bare measurements—and the argument uses the external theorem without circularity. The logic is consistent and the conclusion follows from the recurrence property. A minor soft spot is the precise modeling of the steady regime and the cycle closure; the derivation indicates it works, but one would want to confirm that the recurrence applies without additional assumptions on the operators. It's not a deal-breaker, just worth verifying. This is for researchers in quantum thermodynamics interested in measurement-driven devices. Readers will get a clear limit on what steady cycles can achieve. It deserves a serious referee because the result is mathematically grounded and points to necessary design choices. I recommend sending it to peer review. The no-go is worth documenting properly.

Referee Report

0 major / 2 minor

Summary. The manuscript claims to prove a no-go theorem for work extraction in quantum heat engines powered purely by bare quantum measurements (no feedback or thermal contact) in the steady regime. For a finite-dimensional working substance, a Poincaré-like recurrence theorem for general quantum channels is invoked to show that repeated measurements drive the system to a fixed point of the measurement channel; at this point the state is invariant, measurements are nondisturbing, and no net energy is injected, so no work can be extracted. The result is presented as demonstrating the necessity of an entropy-decreasing process for steady-cycle operation.

Significance. If the central derivation is gap-free, the result is significant for quantum thermodynamics: it supplies a parameter-free, channel-theoretic argument that measurement back-action alone cannot sustain work extraction in steady state. The explicit use of recurrence theorems on quantum channels, rather than ad-hoc assumptions, is a methodological strength that makes the no-go falsifiable and general within the stated scope (finite dimension, bare measurements, no external driving).

minor comments (2)

[Main text, proof of the no-go result] The abstract states that the recurrence theorem implies measurements become nondisturbing at the fixed point, but the main text should include an explicit step showing that the average energy change vanishes identically once the state lies in the support of the fixed point (rather than leaving this as an immediate corollary).
[Introduction and model definition] The assumption that the cycle consists solely of repeated bare measurements without any intermediate unitary or thermal step is load-bearing; a short paragraph clarifying why this excludes all standard engine cycles would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment, accurate summary of our central result, and recommendation of minor revision. The referee's description correctly captures the scope and the Poincaré-recurrence argument for the no-go theorem in the steady regime. No specific technical objections or requested modifications were raised.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central derivation applies an external Poincaré-like recurrence theorem for general quantum channels to establish that repeated bare measurements drive the finite-dimensional working substance to a fixed point of the measurement channel. At this fixed point the state is invariant, backaction vanishes on average, and no net energy is injected, precluding work extraction in the steady regime. The theorem is invoked as an independent mathematical result rather than derived from or defined in terms of the engine's work output or fitted parameters. The steady regime is characterized directly by the channel's fixed-point property under the paper's assumptions (no feedback, no thermal contact, bare measurements only), without circular reduction. No self-citations are load-bearing for the no-go claim, no ansatzes are smuggled, and no empirical patterns are renamed as derivations. The argument remains self-contained against the stated external theorem and assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the existence and applicability of a Poincaré-like recurrence theorem for general quantum channels to the measurement-driven engine; no free parameters or invented entities are introduced.

axioms (1)

standard math Poincaré-like recurrence theorem for general quantum channels
Invoked to establish that repeated measurements drive the system to a fixed point where the channel acts nondisturbingly.

pith-pipeline@v0.9.0 · 5430 in / 1205 out tokens · 62211 ms · 2026-05-08T11:52:28.878279+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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We do not retain the outcome of the measurement

We perform a measurement on the working sub- stance to inject energy through the backaction of the measurement. We do not retain the outcome of the measurement. Such a nonselective quan- tum measurement is described by a completely pos- itive and trace-preserving (CPTP) mapρ→˜ρ (1) = M(1)(ρ)
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Under this control, the working substance evolves unitarily as ˜ρ(1) →ρ (1) =U (1)(˜ρ(1))

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